converting units of time problem solving

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Course: 4th grade   >   Unit 14

• Converting units of time
• Convert to smaller units (sec, min, & hr)
• Time word problem: travel time
• Time word problem: Susan's break

Time conversion word problems

• Converting units of time review (seconds, minutes, & hours)
• Your answer should be
• an integer, like 6 ‍  
• an exact decimal, like 0.75 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  

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Resources tagged with: Time

There are 91 NRICH Mathematical resources connected to Time , you may find related items under Measuring and calculating with units .

Matching Time

Try this matching game which will help you recognise different ways of saying the same time interval.

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Olympic Starters

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

The Time Is ...

Can you put these mixed-up times in order? You could arrange them in a circle.

What Is the Time?

Can you put these times on the clocks in order? You might like to arrange them in a circle.

Order, Order!

Can you place these quantities in order from smallest to largest?

Times of Day

These pictures show some different activities that you may get up to during a day. What order would you do them in?

Try this version of Snap with a friend - do you know the order of the days of the week?

Stop the Clock

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Thousands and Millions

Here's a chance to work with large numbers...

All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

These clocks have only one hand, but can you work out what time they are showing from the information?

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

An Unhappy End

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

John's Train Is on Time

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

5 on the Clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Take a Message Soldier

A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?

These clocks have been reflected in a mirror. What times do they say?

Which Twin Is Older?

A simplified account of special relativity and the twins paradox.

Wonky Watches

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How Many Times?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

The Hare and the Tortoise

In this version of the story of the hare and the tortoise, the race is 10 kilometres long. Can you work out how long the hare sleeps for using the information given?

Back to School

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

A Flying Holiday

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

A Calendar Question

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?

Nirmala and Riki live 9 kilometres away from the nearest market. They both want to arrive at the market at exactly noon. What time should each of them start riding their bikes?

Practice Run

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Train Timetable

Use the information to work out the timetable for the three trains travelling between City station and Farmland station.

Palindromic Date

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Millennium Man

Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?

Hike and Hitch

Fifteen students had to travel 60 miles. They could use a car, which could only carry 5 students. As the car left with the first 5 (at 40 miles per hour), the remaining 10 commenced hiking along the road (at 4 miles per hour)...

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

These two challenges will test your time-keeping!

Friday 13th

Can you explain why every year must contain at least one Friday the thirteenth?

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

Crossing the Atlantic

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

A Child Is Full of ...

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Digital Times

Which segment on a digital clock is lit most each day? Which segment is lit least? Does it make any difference if it is set to 12 hours or 24 hours?

A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

Ten Green Bottles

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

How Many Days?

How many days are there between February 25th 2000 and March 11th?

Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

How to convert units of time

A straightforward guide to units of time and their relation to each other

Author Tess Loucka

Published October 20, 2023

How to Convert Units of Time

Published Oct 11, 2023

Published October 11, 2023

• Key takeaways
• Units of time are the numerical values we use to measure time.
• When converting a larger unit of time to a smaller unit, multiply. When converting a smaller unit to a larger unit, divide. 
• Months are standardized to all have 30 days in time-conversion problems.

Table of contents

Understanding units of time

• Practice problems

Have you ever wondered how old you are? I mean, how old you are really ? How many weeks, days, hours, minutes and seconds old you are? 

Knowing how to convert units of time is essential for answering questions like how old you are down to the day. It also comes in handy when marking your calendar for a date in the future or simply reading a clock to tell the time. 

Converting units of time is one math topic that you’ll use every day throughout your life! So, what exactly is a unit of time anyway?

A unit of time a numerical value we use to measure time. Units of time include seconds, minutes, hours, days, weeks, months and years. 

When thinking about how many seconds in a minute , or how many seconds in an hour , what you’re really thinking about are time unit conversions. 

Before we get into unit conversion, let’s go over the values of each unit of time.

1 minute = 60 seconds

1 hour = 60 minutes

• 1 day = 24 hours

1 week = 7 days

• 1 month = 30 days 
• 1 year = 12 months

You may be wondering why we say one month is equal to 30 days when we know that’s not always true. For the purpose of standardization, months are said to be 30 days long when calculating time conversion. 

Additionally, even though some years are leap years that contain one additional day, we always treat one year as equal to 365 days during time unit conversions.

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A general rule of thumb for time conversion is to multiply when converting a larger unit to a smaller unit and divide when converting a smaller unit to a larger unit. 

For instance, to convert 1 hour into minutes, you’d multiply by 60 because there are 60 minutes in an hour. For example, if we want to know how many minutes are in 3 hours, we’d follow this formula:

3 x 60 = 120 minutes

On the contrary, to convert minutes into hours, you’d divide the amount of minutes by 60. 

How many hours are in 420 minutes?

To solve this problem, all we need to do is divide 420 by 60.

420 / 60 = 7

So there are 7 hours in 420 minutes.

Another thing to remember is that time on a clock always revolves around the number 60. There are 60 seconds and 60 minutes on a clock face, so when we convert seconds to minutes or minutes to hours, we’ll use the number 60 quite a bit.  

Converting seconds to minutes

To convert seconds to minutes, remember two key things:

• There are 60 seconds in 1 minute. Always use the number 60 when converting seconds to minutes.

Ex. Convert 100 seconds to minutes . Divide 100 by 60. Sixty goes into 100 one time. The remainder is 40. So, 100 seconds is equal to 1 minute and 40 seconds. 

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Converting minutes to seconds

Converting minutes to hours.

Two tips to remember: 

• 60 minutes = 1 hour
• We are going from a smaller unit of time to a larger unit of time, so we have to divide!

Ex. Convert 240 minutes to hours. Divide 240 by 60 to get 4. That means 4 hours equals 240 minutes.

Converting hours to minutes

Two tips to remember:

• We are going from a larger unit of time to a smaller unit of time, so multiply!

Ex. Convert two and a half hours to minutes . Multiply 2 by 60 to get 120. Add 30 minutes. 120+30=150. There are 150 minutes in two and a half hours.

Converting hours to days

• 24 hours = 1 day

Ex. Convert 28 hours to days . Divide 28 by 24. Twenty-four goes into 28 one time. The remainder is 4. So, there is 1 day and 4 hours in 28 hours.

Converting days to hours

Ex. Convert 7 days to hours. Multiply 7 by 24 to get 168. That means 168 hours equals 7 days.

Converting days to weeks

• 7 days = 1 week

Ex. Convert 35 days to weeks. Thirty-five divided by 7 is 5. That means 5 weeks equals 35 days.

Converting weeks to days

Ex. Convert 2 weeks and 3 days into days. Two multiplied by 7 is 14. Add 3 to get 17. There are 17 days in 2 weeks and 3 days.

Converting weeks to months

• 4 weeks = 1 month

Ex. Convert 6 weeks to months. Six divided by 4 is 1 with a remainder of 2. So, there is 1 month and 2 weeks in 6 weeks. 

Converting months to weeks

• 1 month = 4 weeks

Ex. Convert 8 months to weeks. Eight multiplied by 4 is 32. So, there are 32 weeks in 8 months.

Converting months to years

• 12 months = 1 year

Ex. Convert 24 months to years. Twenty-four divided by 12 is 2. That means 2 years equals 24 months.

Converting years to months

Ex. Convert 10 years to months. Multiply 10 by 12 to get 120. That means 120 months equals 10 years.

How to convert non-consecutive units of time

By now, we’ve gone over the rules for converting consecutive units of time, like minutes to seconds, or months to years. But what about non-consecutive conversion? How do you convert minutes to months? Or seconds to hours? 

To convert non-consecutive units, start with the larger unit and work your way down to the smaller unit. Breaking the problem down into smaller problems helps us! 

Let’s try turning one week into seconds:

Start by converting 1 week into hours. Since we are going from a larger unit of time to a smaller unit of time, we multiply:

1 day = 24 hours 

Therefore, we multiply 7 x 24 to get 168 hours in one week.

Next, let’s convert 168 hours into minutes. Once again, we are going from large to small so we multiply.

Therefore, we multiply 60 minutes by 168 hours to get 10,080 minutes.

For the last step, convert 10,080 minutes into seconds. You guessed it! We multiply again

Multiply 60 seconds by 10,080 minutes to get 604,800 seconds.

In other words:

7 days x 24 hours = 168 hours

168 hours x 60 minutes = 10,080 minutes

10,080 minutes x 60 seconds = 604,800 seconds

So, there are 604,800 seconds in 1 week. 

Converting units of time questions

Answer: 10,080

Start with the largest unit of time and work down to the smallest. There are 7 days in one week. Each day, there are 24 hours. In each hour there are 60 minutes. 7x24x60=10,080.

Answer: 8,100

Start with the largest unit of time and work down to the smallest. In 1 hour, there are 60 minutes. That means 2 hours equals 120 minutes. Add 15 minutes to that to get 135 minutes. There are 60 seconds in each minute. 135×60=8,100.

Answer: 436

Start with the largest unit of time and work down to the smallest. In 1 year, there are 365 days. Every month counts as 30 days, so 2 months equals 60 days. 365+60=425. Add 11 days to that to get 436.

FAQs about converting time

Seconds, minutes, hours, days, weeks, months, and years.

The zeptosecond. A zeptosecond is a trillionth of a billionth of a second. However, the second is the smallest unit of time we use on a daily basis.

There are 60 minutes in an hour, so to convert hours to minutes, multiply by 60. When converting minutes to hours, you divide.

Try DoodleMaths for free!

Lesson credits

Tess Loucka

Tess Loucka discovered her passion for writing in school and has not stopped writing since. Combined with her love of numbers, she became a maths and English tutor. Since graduating, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.

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Converting Units of Time

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Online Math Activity - Converting Units of Time

Get ready to practice converting units of time with your third grade class! Students will practice converting days to weeks, hours to days, minutes to hours, and so on in this digital math game. Here are a few sample math questions your students may be expected to answer in this telling time activity:

• "Drag and drop the symbol that makes the number sentence true. 300 minutes is [greater than, less than, or equal to] 3 hours."
• "Dayton's baby sister is six weeks old. How many days are in six weeks?"
• "Convert from minutes to hours. [Blank] minutes equals 9 hours."
• "How many minutes are in 2 hours?"
• "Cyrus slept for eight hours last night. How many minutes are in eight hours?"

As students work their way through the math activity, they can count on plenty of handy features to help them make the most out of their math practice session:

• Hint Button - When children get stuck on a question and need a little help, they can click on the Hint Button. The hint consists of a written or pictorial clue that will point children in the right direction without giving away the answer.
• Explanation Page - Students are bound to get an answer wrong every now and then. When they do, a detailed explanation page pops up on the practice screen to show them the correct answer, accompanied by an easy-to-understand explanation to help them learn from mistakes.
• Progress-Tracker - Students can check out the progress-tracker in the upper-right corner of their practice screen to see how many questions they have answered so far out of the total number of questions in the math activity.
• Score-Tracker - Children can view the score-tracker beneath the progress-tracker to see how many points they have earned for correct solutions.
• Speaker Icon - To hear the math question read out loud in a clear voice, students can click on the speaker icon in the upper-left corner of the practice screen. This feature is a great option for ESL/ELL students and children who are auditory processors.

All of these features have been carefully designed to help your third grade students achieve more in their online math practice.

Digital Math Practice Makes Learning Exciting

Give your class a reason to get excited about math practice with interactive math games from I Know It ! Whether you are an elementary math teacher, homeschool educator, or school administrator, we're confident you will love using the I Know It online math program with your students. Check out a few highlights of our program from an educator's perspective:

• Choose from hundreds of math lessons covering dozens of foundational elementary math topics from kindergarten to fifth grade.
• Browse math lessons that have been written by accredited elementary math teachers to meet Common Core Standards.
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Students, too, have lots to love about the I Know It digital math program:

• Adorable, animated characters dance around on the practice screen and do a clever trick when students submit a correct solution to a math problem.
• Plenty of positive feedback messages spur students on in their math practice even when they make mistakes.
• Bright colors and a bold, kid-friendly math lesson format presents each practice session as a fun, yet challenging math game... and more!

We hope you and your students will enjoy converting units of time in this online math lesson. Be sure to browse the hundreds of other 3rd grade elementary skill practice lessons in our collection as well.

Test the Waters or Dive Right In

Looking for a way to "test the waters" and see if the I Know It digital math practice program is right for you and your class? Sign up for a free thirty-day trial and try out this telling time game, as well as all of the math lessons available on our website, at no cost for a full thirty days! We're confident you and your students will love experiencing the difference interactive math practice can make. In fact, when your free trial ends, we hope you won't hesitate to join our community as a member. This way, your class can continue to enjoy the benefits of digital math practice for a full calendar year. We offer membership options for families, individual teachers, schools, and school districts. Visit our membership information page for details: https://www.iknowit.com/order.html .

Your I Know It membership unlocks the program's extensive administrator tools. You will discover a plethora of handy features in your parent or teacher administrator account that help you create a class roster and add your students to it, change basic math lesson settings, monitor student progress with detailed statistics, print, download, and email student progress reports, and much more. These administrator tools serve to help you customize your class's math practice experience.

Your students will log into I Know It with their unique username and password. From a kid-friendly version of the homepage, they can quickly find and launch math activities you have assigned to them for practice. If you choose to give them permission through your parent or teacher administrator account, students can also explore other math activities at their grade level and beyond for additional practice or an extra challenge. Grade levels in the student mode of I Know It are labeled with letters instead of numbers (i.e., "Level C" for third grade), making it easy for you to assign math lessons based on each child's needs and skill level.

This math lesson is categorized as Level C. It may be ideal for a third grade class.

Common Core Standard

3.MD.1, MA.4.M.1.2, MA.5.M.1.1, 3.7C Measurement And Data Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

You might also be interested in...

Telling Time (Nearest 5 Minutes) (Level C) In this third grade-level math lesson, students will practice telling time to the nearest five minutes. Questions are presented in multiple-choice format and fill-in-the-blank format.

Telling Time (Nearest Minute) (Level C) In this math lesson geared toward third grade, students will practice telling time to the nearest minute. Questions are presented in fill-in-the-blank format and multiple-choice format.

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CONVERSION OF UNITS OF TIME PRACTICE PROBLEMS

Convert the following into minutes :

Example 1 :

1 hour  =  60 minutes

13 hrs  =  (13 × 60) min

13 hrs  =  780 min

Example 2 :

1560 seconds

1 minute  =  60 seconds

1560 s  =  [1560/60] min

1560 s =  26 min

Example 3 :

1 day  =  1440 minutes

2 days  =  (1440 × 2) min

2 days  =  2880 min

Example 4 :

6 hours 17 minutes

6 hrs  =  360 min

6 hours 17 minutes  =  (360 + 17) min

6 hours 17 minutes  =  377 min

Example 5 :

3 days 5 hours 38 minutes

3 days  =  (1440 × 3) min

3 days  =  4320 min

5 hrs  =  (60 × 5) min

5 hrs  =  300 min

3 days 5 hours 38 minutes  =  (4320 + 300 + 38) min

3 days 5 hours 38 minutes  =  4658 min

Convert the following into days :

Example 6 :

1 year  =  365 days

8 years  =  2 leap years + 6 years

2 Leap year  =  (366 × 2) days

2 Leap year  =  732 days

6 years  =  (365 × 6) days

6 years  =  2190 days

=  (732 + 2190) days

=  2922 days

8 years  =  2922 days

Example 7 :

4320 minutes

4320 minutes  =  (4320/1440) days

4320 min  =  3 days

Example 8 :

24 hrs  =  1 day

864 hrs  =  (864/24) days

=  36 days

864 hrs  =  36 days

Example 9 :

1 day  =  86400 seconds

864000 seconds  =  (864000/86400) days

=  10 days

864000 s  =  10 days

Convert the following into seconds :

Example 10 :

1 hr  =  3600 seconds

3 hrs  =  (3 × 3600) s

3 hrs  =  10800 s

Example 11 :

47 min  =  (47 × 60) s

47 min  =  2820 s

Example 12 :

5 hours 7 minutes

1 hour  =  3600 seconds

5 hrs  =  (5 × 3600) s

5 hrs  =  18000 s

7 min  =  (7 × 60) s

7 min  =  420 s

5 hours 7 minutes  =  (18000 + 420) s

5 hours 7 minutes  =  18420 s

Example 13 :

7 days  =  (7 × 86400) s

7 days  =  604800 s

1 week  =  7 days

1 week  =  604800 s

5 weeks  =  (5 × 604800) s

5 weeks  =  3024000 s

Which time period is longer :

Example 14 :

1000 seconds or 16 minutes

1000 s  =  (1000/60)

1000 s  =  16.67 min

16.67 min > 16 minutes

1000 seconds period is longer

Example 15 : 

6 hours or 20000 seconds

6 hrs  =  (6 × 3600) s

6 hrs  =  21600 s

21600 s > 20000 s

6 hours period is longer

Example 16 : 

2 weeks or 20000 minutes

7 days  =  (7 × 1440) min

7 days  =  10080 min

1 week  =  10080 min

2 weeks  =  20160 min

20160 min > 20000 min

2 weeks period is longer

Example 17 : 

5 days 7 hours or 8000 minutes ?

5 days  =  (5 × 1440) min

5 days  =  7200 min

1 hr  =  60 minutes

7 hrs  =  (7 × 60) min

7 hrs  =  420 min

5 days 7 hours  =  (7200 + 420) min

5 days 7 hours  =  7620 min

7620 min < 8000 min

8000 minutes period is longer

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Converting units of time

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Seconds, minutes, hours, days, weeks and years

These grade 3 time worksheets give students practice in converting units of time  between seconds, minutes, hours, days, weeks and years. 

Minutes & seconds:

Hours & minutes:

Hours & seconds:

Hours & days:

Weeks & days:

Years & days:

More time and calendar worksheets

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25 Time Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma Johnson

Time word problems are an important element of teaching children how to tell the time. Children are introduced to the concept of time in Year 1. At this early stage, they learn the basics of analogue time; reading to the hour and half past and learn how to draw hands on the clocks to show these times.

As they move through primary school, pupils progress onto reading the time in analogue, digital and 24 hour clocks and being able to compare the duration of events. By the time children reach upper Key Stage 2, they should be confident in reading the time in all formats and solving problems involving converting between units of time.

Time in Year 1

Time in year 2, time in year 3, time in year 4, time in year 5 & 6.

• Why are word problems important for children’s understanding of time

How to teach time word problem solving in primary school

Time word problems for year 2, time word problems for year 3, time word problems for year 4, time word problems for year 5, time word problems for year 6, more time and word problems resources.

Let's Practice Telling The Time

Download this free printable worksheet to let your students practice telling the time.

When students are first introduced to time and time word problems , it is important for them to have physical clocks, to hold and manipulate the hands. Pictures on worksheets are helpful, but physical clocks enable them to work out what is happening with the hands and to solve word problems involving addition word problems and subtraction word problems .

Time word problems are important for helping children to understand how time is used in the real-world. We have put together a collection of 25 time word problems, which can be used with pupils from Year 2 to Year 6.

Time word problems in the National Curriculum  

In Year 1, students are introduced to the basics of time. They learn to recognise the hour and minute hand and use this to help read the time to the hour and half past the hour. They also draw hands on clock faces to represent these times. 

By the end of Year 2, pupils should be able to tell the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. They should also know the number of minutes in an hour and the number of hours in a day.

In Year 3, children read the time in analogue (including using Roman Numerals). By this stage they are also learning to read digital time in 12 and 24 hour clock, using the AM and PM suffixes. Pupils record and compare time in terms of seconds, minutes and hours; know the number of seconds in a minute, days in a month and year and compare durations of events.

By Year 4, pupils should be confident telling the time in analogue to the nearest minute, digital and 24 hour clock. They also need to be able to read, write and convert time between analogue and digital 12 and 24 hour clocks and solve problems involving converting from hours to minutes; minutes to seconds; years to months and weeks to days. 

By Year 5 and 6, there is only limited mention of time in the curriculum. Pupils continue to build on the knowledge they have picked up so far and should be confident telling the time and solving a range of problems, including: converting units of time; elapsed time word problems, working with timetables and tackling multi-step word problems .

Time word problems have been known to appear on Year 6 SATs tests. Third Space Learning’s online one-to-one SATs revision programme incorporates a wide range of word problems to develop students’ problem solving skills and prepare them the SATs tests. Available for all primary year groups as well as Year 7 and GCSE, our online tuition programmes are personalised to suit the needs of each individual student, fill learning gaps and build confidence in maths.

Why are word problems important for children’s understanding of time

Word problems are important for helping children to develop their understanding of time and the different ways time is used on an every-day basis. Confidence in telling the time and solving a range of time problems is a key life skill. Time word problems provide children with the opportunity to build on the skills they have picked up and apply them to real-world situations.

It’s important children learn the skills needed to solve word problems. Key things they need to remember are: to make sure they read the question carefully; to think whether they have fully understood what is being asked and then identify what they will need to do to solve the problem and whether there are any concrete resources or pictorial representations which will help them.

Here is an example:

Mr Arrowsmith drives to Birmingham. He sets off at 3:15pm. He stops for a break of 15 minutes at 4:50 and arrives in Birmingham at 6:15pm.

How long did Mr Arrowsmith spend driving?

How to solve:

What do you already know?

• We know that he set off at 3:15pm and stopped for a break at 4:50. We can calculate how long the first part of his journey was, by counting on from 3:15 to 4:50.
• He had a break at 4:50pm for 15 minutes, so we won’t include that in our driving time calculation.
• He then must have set off again at 5:05pm, before arriving at 6:15pm. We can use this information to work out the length of the second part of his journey.
• We can then add the 2 journey times together, to calculate the total amount of time spent driving. 

How can this be represented pictorially?

•  We can use a number line to calculate the length of time each journey takes.
• If we start by adding on an hour, we can then calculate how many more minutes for each section of the journey.
• Once we have calculated the journey time for each part of the journey, we can add these together to calculate the total journey time.

Time word problems in Year 2 require students to read the time to o’clock and half past the hour and compare and sequence time intervals. 

Oliver went for a bike ride with his friend. 

He left home at 2 o’clock and came home at 4 o’clock.

How long was he out on his bike for?

Answer: 2 hours

Count on from 2 o’ clock to 4 o’clock or subtract 2 from 4.

Mum went shopping at 3 o’clock and got home an hour later.

Draw the time she got home on the clock below.

Tom baked a cake.

The cake was in the oven for one hour. 

If he took the cake out at half past 11, what time did he put the cake in?

Answer: Half past 10

Use an hour from half past 11.

Arlo starts school at 9 o’clock and has his first break at half past 10. 

How long does he have to wait for his first break?

Answer: One and a half hours.

(Use a number line to count on from 9 to half past 10)

The Smith family are going to the beach.

They plan to leave home at 10 o’clock and the journey take two hours.

What time will they arrive at the beach?

Answer: 12 o’clock

(Use a number line to count on 2 hours from 10 o’clock)

With time word problems for year 3 , students build on their understanding of analogue time from Year 2 and also begin to  read the time in  digital (12 and 24 hour clock). Children also need to be able to compare time and durations of events.

Chloe is walking to football training.

She sets off at 8:40am and takes 17 minutes to get there.

What time does she arrive?

Answer: 8:57

(Count on 17 minutes from 8:40 – use a number line if needed)

(Picture of analogue clock with 2:30 showing here)

Maisie says that in 1 hour and 48 minutes it will be 4:28.

Do you agree? Explain how you worked out your answer.

Answer: Maisie is wrong. It will be 4:18. 

This can be worked out by counting on an hour from 2:30 to 3:30 and then another 48 minutes to 4:18.

The Baker family are driving to their campsite. 

They set off at 8:30 am, drive for 2 hours and 15 minutes, then had a 30 minute break. 

If they drive for another 1 hour and 45 minutes, what time do they arrive at the campsite?

Answer: 12:45pm

Use a number line to show what time they arrive at the break. From 8:30, count on 2 hours and 15 minutes to get to 10:45. Add on the 30 minute break. It is now 11:15. They count on another hour and a half  to 12:45

Ahmed looks at his watch and says ‘it is half past 4 in the afternoon’

Jude says that it is 17:30 in a 24 hour clock.

Is Jude correct? Explain your answer.

Answer: Jude is not correct. Half past 4 in the afternoon is 16:30 not 17:30

How many minutes are there in 2 hours and 30 minutes?

Answer: 150 minutes

60 + 60 + 30 = 150

When solving time word problems for year 4 , pupils need to be confident telling time in analogue, and digital, as well as converting between analogue, 12 hour and 24 hour clock. They also begin to solve more challenging problems involving duration of time and converting time.

If there are 60 seconds in 1 minute. How many seconds are there in 8 minutes?

Answer: 480 seconds

60 x 8 = 480 seconds (calculate 6 x 8, then multiply by 10)

Mason played on his VR from 3:35 to 5:25.

How long did he play on his VR?

Answer: 1 hour and 50 minutes.

Count on from 3:35 (using a numberline if needed)

Jamie started his homework at 3:45pm. He finished 43 minutes later.

What time did Jamie finish? Give your answer in 24 hour clock.

Answer: 16:28

Count on 43 minutes from 3:45 (use a number line, if needed) = 4:28. Convert to 24 hour clock.

Chloe and Freya went to the cinema to watch a film. The film started at 2:05pm and lasted for 1 hour and 43 minutes. 

What time did the film end?

Answer: 3:48pm

Count on one hour from 2:05 pm to 3:05pm, then add another 43 minutes – 3:48pm

A family is driving on their holiday.

They drive for 2 hours and 28 minutes, stop for 28 minutes and then drive a further 1 hour and 52 minutes.

If they left at 8:30am, what time did they arrive?

Answer: 1:18pm

2 hours and 28 minutes from 8:30am = 10:58am

10:58am with a 28 minute break = 11:26am

1 hour 52 minute drive from 11:26 am = 1:18pm

With word problems for year 5 , pupils should be confident telling the time in analogue and digital and solving a wider range of time problems including: converting units of time; interpreting and answering questions on timetables and elapsed time.

The sun set at 19:31 and rose again at 6:28. 

How many hours passed between the sun setting and rising again?

Answer: 10 hours and 57 minutes

Count on from 19:31 to 5:31 (10 hours)

Then count on from 5:31 to 6:28 (57 minutes)

A play started at 14:45 and finished at 16:58.

How long was the play?

Answer: 2 hours and 13 minutes

Count on 2 hours from 14:45 to 16:45, then add another 13 minutes to get to 16:58

How many seconds are there in 23 minutes?

Answer: 1380 seconds

Show as column method: 60 x 23 = 1380

Max ran a race in 2 minutes 13 seconds, Oscar ran it in 125 seconds. 

What was the difference in time between Max and Oscar?

Answer: Oscar was 8 seconds faster.

Max – 2 minutes 13 seconds, Oscar – 2 minutes 5 seconds (difference of 8 seconds)

4 children take part in a freestyle swimming relay.

There times were: 

Maisie: 42.8 seconds

Amber 36.3 seconds

Megan 48.7 seconds

Zymal 45.6 seconds

What was the final time for the relay in minutes and seconds?

Answer: 2:53.4

(Show as column method) 42.8 + 36.3 + 48.7 + 45.6 = 173.4 seconds

173.4 seconds = 2:53.4

No new time concepts are taught to pupils in word problems for year 6 . By this stage they are continuing to build confidence and develop skills within the concepts already taught.

Chess: 25 minutes

Basketball: 40 minutes.

Trampolining: 30 minutes

Gymnastics: 50 minutes

Tennis 40 minutes

Tri golf – 45 minutes

Hamza is choosing activities to take part in at his holiday club.

The activities can’t add up to more than 2 hours.

Which 3 activities could he do, which add up to exactly 2 hours?

Answer: Trampolining, gymnastics and tennis: Trampolining: 30 minutes, gymnastics: 50 minutes, tennis: 40 minutes.

5 children took part in a sponsored swim. The children swam for the following lengths of time:

Sam: 27 minutes 37 seconds

Jemma: 33 minutes 29 seconds.

Ben: 23 minutes 18 seconds

Lucy: 41 minutes 57 seconds

Oliver: 39 minutes 21 seconds

Answer: 18 minutes 30 seconds

Longest: Lucy: 41 minutes 57 seconds

Shortest: Ben: 23 minutes 18 seconds.

Difference – count up from 23 minutes 18 seconds to 41 minutes 57 seconds = 18 minutes 39 seconds

What is 6 minutes 47 seconds in seconds?

Answer: 407 minutes

60 x 6 = 360

360 + 47 = 407 minutes

Bethany’s goal is to run round her school running track in under 8 minutes.

She runs it in 440 seconds. Does she achieve her goal? How far above or below the target is she?

Answer: Bethany beats her target by 40 seconds

8 minutes = 8 x 60 = 480 minutes

Lucy’s favourite programme is on TV twice a week for 35 minutes. 

In 6 weeks, how many hours does Lucy spend watching her favourite programme?

Answer: 7 hours

420 minutes = 7 hours

(Show as column method) 35 x 12 = 420 minutes

420 ÷ 60 = 7 

For more time resources, take a look at our collection of printable time worksheets. Third Space Learning also offers a wide collection of word problems covering a range of topics such as place value, decimals and fractions word problems , percentages word problems , division word problems , ratio word problems , addition and subtraction word problems , multiplication word problems , money word problems and other word problem challenge cards.

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Chapter 1: Algebra Review

1.6 Unit Conversion Word Problems

One application of rational expressions deals with converting units. Units of measure can be converted by multiplying several fractions together in a process known as dimensional analysis.

The trick is to decide what fractions to multiply. If an expression is multiplied by 1, its value does not change. The number 1 can be written as a fraction in many different ways, so long as the numerator and denominator are identical in value. Note that the numerator and denominator need not be identical in appearance, but rather only identical in value. Below are several fractions, each equal to 1, where the numerator and the denominator are identical in value. This is why, when doing dimensional analysis, it is very important to use units in the setup of the problem, so as to ensure that the conversion factor is set up correctly.

Example 1.6.1

 If 1 pound = 16 ounces, how many pounds are in 435 ounces?

[latex]\begin{array}{rrll} 435\text{ oz}&=&435\cancel{\text{oz}}\times \dfrac{1\text{ lb}}{16\cancel{ \text{oz}}} \hspace{0.2in}& \text{This operation cancels the oz and leaves the lbs} \\ \\ &=&\dfrac{435\text{ lb}}{16} \hspace{0.2in}& \text{Which reduces to } \\ \\ &=&27\dfrac{3}{16}\text{ lb} \hspace{0.2in}& \text{Solution} \end{array}[/latex]

The same process can be used to convert problems with several units in them. Consider the following example.

Example 1.6.2

A student averaged 45 miles per hour on a trip. What was the student’s speed in feet per second?

[latex]\begin{array}{rrll} 45 \text{ mi/h}&=&\dfrac{45\cancel{\text{mi}}}{\cancel{\text{hr}}}\times \dfrac{5280 \text{ ft}}{1\cancel{ \text{mi}}}\times \dfrac{1\cancel{\text{hr}}}{3600\text{ s}}\hspace{0.2in}&\text{This will cancel the miles and hours} \\ \\ &=&45\times \dfrac{5280}{1}\times \dfrac{1}{3600} \text{ ft/s}\hspace{0.2in}&\text{This reduces to} \\ \\ &=&66\text{ ft/s}\hspace{0.2in}&\text{Solution} \end{array}[/latex]

Example 1.6.3

Convert 8 ft 3 to yd 3 .

[latex]\begin{array}{rrll} 8\text{ ft}^3&=&8\text{ ft}^3 \times \dfrac{(1\text{ yd})^3}{(3\text{ ft})^3}&\text{Cube the parentheses} \\ \\ &=&8\text{ }\cancel{\text{ft}^3}\times \dfrac{1\text{ yd}^3}{27\text{ }\cancel{\text{ft}^3}}&\text{This will cancel the ft}^3\text{ and replace them with yd}^3 \\ \\ &=&8\times \dfrac{1\text{ yd}^3}{27}&\text{Which reduces to} \\ \\ &=&\dfrac{8}{27}\text{ yd}^3\text{ or }0.296\text{ yd}^3&\text{Solution} \end{array}[/latex]

Example 1.6.4

A room is 10 ft by 12 ft. How many square yards are in the room? The area of the room is 120 ft 2 (area = length × width).

Converting the area yields:

[latex]\begin{array}{rrll} 120\text{ ft}^2&=&120\text{ }\cancel{\text{ft}^2}\times \dfrac{(1\text{ yd})^2}{(3\text{ }\cancel{\text{ft}})^2}&\text{Cancel ft}^2\text{ and replace with yd}^2 \\ \\ &=&\dfrac{120\text{ yd}^2}{9}&\text{This reduces to} \\ \\ &=&13\dfrac{1}{3}\text{ yd}^2&\text{Solution} \\ \\ \end{array}[/latex]

The process of dimensional analysis can be used to convert other types of units as well. Once relationships that represent the same value have been identified, a conversion factor can be determined.

Example 1.6.5

A child is prescribed a dosage of 12 mg of a certain drug per day and is allowed to refill his prescription twice. If there are 60 tablets in a prescription, and each tablet has 4 mg, how many doses are in the 3 prescriptions (original + 2 refills)?

[latex]\begin{array}{rrll} 3\text{ prescriptions}&=&3\cancel{\text{pres.}}\times \dfrac{60\cancel{\text{tablets}}}{1\cancel{\text{pres.}}}\times \dfrac{4\cancel{\text{mg}}}{1\cancel{\text{tablet}}}\times \dfrac{1\text{ dosage}}{12\cancel{\text{mg}}}&\text{This cancels all unwanted units} \\ \\ &=&\dfrac{3\times 60\times 4\times 1}{1\times 1\times 12}\text{ or }\dfrac{720}{12}\text{ dosages}&\text{Which reduces to} \\ \\ &=&60\text{ daily dosages}&\text{Solution} \\ \\ \end{array}[/latex]

Metric and Imperial (U.S.) Conversions

[latex]\begin{array}{rrlrrl} 12\text{ in}&=&1\text{ ft}\hspace{1in}&10\text{ mm}&=&1\text{ cm} \\ 3\text{ ft}&=&1\text{ yd}&100\text{ cm}&=&1\text{ m} \\ 1760\text{ yds}&=&1\text{ mi}&1000\text{ m}&=&1\text{ km} \\ 5280\text{ ft}&=&1\text{ mi}&&& \end{array}[/latex]

Imperial to metric conversions:

[latex]\begin{array}{rrl} 1\text{ inch}&=&2.54\text{ cm} \\ 1\text{ ft}&=&0.3048\text{ m} \\ 1\text{ mile}&=&1.61\text{ km} \end{array}[/latex]

[latex]\begin{array}{rrlrrl} 144\text{ in}^2&=&1\text{ ft}^2\hspace{1in}&10,000\text{ cm}^2&=&1\text{ m}^2 \\ 43,560\text{ ft}^2&=&1\text{ acre}&10,000\text{ m}^2&=&1\text{ hectare} \\ 640\text{ acres}&=&1\text{ mi}^2&100\text{ hectares}&=&1\text{ km}^2 \end{array}[/latex]

[latex]\begin{array}{rrl} 1\text{ in}^2&=&6.45\text{ cm}^2 \\ 1\text{ ft}^2&=&0.092903\text{ m}^2 \\ 1\text{ mi}^2&=&2.59\text{ km}^2 \end{array}[/latex]

[latex]\begin{array}{rrlrrl} 57.75\text{ in}^3&=&1\text{ qt}\hspace{1in}&1\text{ cm}^3&=&1\text{ ml} \\ 4\text{ qt}&=&1\text{ gal}&1000\text{ ml}&=&1\text{ litre} \\ 42\text{ gal (petroleum)}&=&1\text{ barrel}&1000\text{ litres}&=&1\text{ m}^3 \end{array}[/latex]

[latex]\begin{array}{rrl} 16.39\text{ cm}^3&=&1\text{ in}^3 \\ 1\text{ ft}^3&=&0.0283168\text{ m}^3 \\ 3.79\text{ litres}&=&1\text{ gal} \end{array}[/latex]

[latex]\begin{array}{rrlrrl} 437.5\text{ grains}&=&1\text{ oz}\hspace{1in}&1000\text{ mg}&=&1\text{ g} \\ 16\text{ oz}&=&1\text{ lb}&1000\text{ g}&=&1\text{ kg} \\ 2000\text{ lb}&=&1\text{ short ton}&1000\text{ kg}&=&1\text{ metric ton} \end{array}[/latex]

[latex]\begin{array}{rrl} 453\text{ g}&=&1\text{ lb} \\ 2.2\text{ lb}&=&1\text{ kg} \end{array}[/latex]

Temperature

Fahrenheit to Celsius conversions:

[latex]\begin{array}{rrl} ^{\circ}\text{C} &= &\dfrac{5}{9} (^{\circ}\text{F} - 32) \\ \\ ^{\circ}\text{F}& =& \dfrac{9}{5}(^{\circ}\text{C} + 32) \end{array}[/latex]

For questions 1 to 18, use dimensional analysis to perform the indicated conversions.

• 7 miles to yards
• 234 oz to tons
• 11.2 mg to grams
• 1.35 km to centimetres
• 9,800,000 mm to miles
• 4.5 ft 2 to square yards
• 435,000 m 2 to square kilometres
• 8 km 2 to square feet
• 0.0065 km 3 to cubic metres
• 14.62 in. 2 to square centimetres
• 5500 cm 3 to cubic yards
• 3.5 mph (miles per hour) to feet per second
• 185 yd per min. to miles per hour
• 153 ft/s (feet per second) to miles per hour
• 248 mph to metres per second
• 186,000 mph to kilometres per year
• 7.50 tons/yd 2 to pounds per square inch
• 16 ft/s 2 to kilometres per hour squared

For questions 19 to 27, solve each conversion word problem.

• On a recent trip, Jan travelled 260 miles using 8 gallons of gas. What was the car’s miles per gallon for this trip? Kilometres per litre?
• A certain laser printer can print 12 pages per minute. Determine this printer’s output in pages per day.
• An average human heart beats 60 times per minute. If the average person lives to the age of 86, how many times does the average heart beat in a lifetime?
• Blood sugar levels are measured in milligrams of glucose per decilitre of blood volume. If a person’s blood sugar level measured 128 mg/dL, what is this in grams per litre?
• You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet cost $18 per square yard. How much will the carpet cost?
• A cargo container is 50 ft long, 10 ft wide, and 8 ft tall. Find its volume in cubic yards and cubic metres.
• A local zoning ordinance says that a house’s “footprint” (area of its ground floor) cannot occupy more than ¼ of the lot it is built on. Suppose you own a [latex]\frac{1}{3}[/latex]-acre lot (1 acre = 43,560 ft 2 ). What is the maximum allowed footprint for your house in square feet? In square metres?
• A car travels 23 km in 15 minutes. How fast is it going in kilometres per hour? In metres per second?
• The largest single rough diamond ever found, the Cullinan Diamond, weighed 3106 carats. One carat is equivalent to the mass of 0.20 grams. What is the mass of this diamond in milligrams? Weight in pounds?

Answer Key 1.6

Intermediate Algebra Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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