work problem solving grade 8

Math Word Problems with Answers - Grade 8

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"Work" Word Problems

Painting & Pipes Tubs & Man-Hours Unequal Times Etc.

"Work" problems usually involve situations such as two people working together to paint a house. You are usually told how long each person takes to paint a similarly-sized house, and you are asked how long it will take the two of them to paint the house when they work together.

Many of these problems are not terribly realistic — since when can two laser printers work together on printing one report? — but it's the technique that they want you to learn, not the applicability to "real life".

The method of solution for "work" problems is not obvious, so don't feel bad if you're totally lost at the moment. There is a "trick" to doing work problems: you have to think of the problem in terms of how much each person / machine / whatever does in a given unit of time . For instance:

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Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. How long would it take the two painters together to paint the house?

To find out how much they can do together per hour , I make the necessary assumption that their labors are additive (in other words, that they never get in each other's way in any manner), and I add together what they can do individually per hour . So, per hour, their labors are:

But the exercise didn't ask me how much they can do per hour; it asked me how long they'll take to finish one whole job, working togets. So now I'll pick the variable " t " to stand for how long they take (that is, the time they take) to do the job together. Then they can do:

This gives me an expression for their combined hourly rate. I already had a numerical expression for their combined hourly rate. So, setting these two expressions equal, I get:

I can solve by flipping the equation; I get:

An hour has sixty minutes, so 0.8 of an hour has forty-eight minutes. Then:

They can complete the job together in 4 hours and 48 minutes.

The important thing to understand about the above example is that the key was in converting how long each person took to complete the task into a rate.

hours to complete job:

first painter: 12

second painter: 8

together: t

Since the unit for completion was "hours", I converted each time to an hourly rate; that is, I restated everything in terms of how much of the entire task could be completed per hour. To do this, I simply inverted each value for "hours to complete job":

completed per hour:

Then, assuming that their per-hour rates were additive, I added the portion that each could do per hour, summed them, and set this equal to the "together" rate:

adding their labor:

As you can see in the above example, "work" problems commonly create rational equations . But the equations themselves are usually pretty simple to solve.

One pipe can fill a pool 1.25 times as fast as a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?

My first step is to list the times taken by each pipe to fill the pool, and how long the two pipes take together. In this case, I know the "together" time, but not the individual times. One of the pipes' times is expressed in terms of the other pipe's time, so I'll pick a variable to stand for one of these times.

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Since the faster pipe's time to completion is defined in terms of the second pipe's time, I'll pick a variable for the slower pipe's time, and then use this to create an expression for the faster pipe's time:

slow pipe: s

together: 5

Next, I'll convert all of the completion times to per-hour rates:

Then I make the necessary assumption that the pipes' contributions are additive (which is reasonable, in this case), add the two pipes' contributions, and set this equal to the combined per-hour rate:

multiplying through by 20 s (being the lowest common denominator of all the fractional terms):

20 + 25 = 4 s

45/4 = 11.25 = s

They asked me for the time of the slower pipe, so I don't need to find the time for the faster pipe. My answer is:

The slower pipe takes 11.25 hours.

Note: I could have picked a variable for the faster pipe, and then defined the time for the slower pipe in terms of this variable. If you're not sure how you'd do this, then think about it in terms of nicer numbers: If someone goes twice as fast as you, then you take twice as long as he does; if he goes three times as fast as you, then you take three times as long as him. In this case, if he goes 1.25 times as fast, then you take 1.25 times as long. So the variables could have been " f  " for the number of hours the faster pipe takes, and then the number of hours for the slower pipe would have been " 1.25 f  ".

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Quiz 8th-Graders With These Math Word Problems

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Solving math problems can intimidate eighth-graders . It shouldn't. Explain to students that you can use basic algebra and simple geometric formulas to solve seemingly intractable problems. The key is to use the information you are given and then isolate the variable for algebraic problems or to know when to use formulas for geometry problems. Remind students that whenever they work a problem, whatever they do to one side of the equation, they need to do to the other side. So, if they subtract five from one side of the equation, they need to subtract five from the other.

The free, printable worksheets below will give students a chance to work problems and fill in their answers in the provided blank spaces. Once the students have completed the work, use the worksheets to do quick formative assessments  for an entire math class.

Worksheet No. 1

 Deb Russell

Print the PDF :   Worksheet No. 1

On this PDF, your students will solve problems such as:

"5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does 1 hockey puck cost?"

Explain to students that they'll need to consider what they do know, such as the total price of five hockey pucks and three hockey sticks ($23) as well as the total price for five hockey pucks and one stick ($20). Point out to students that they'll start with two equations, with each providing a total price and each including five hockey sticks.

Worksheet No. 1 Solutions

Print the PDF :   Worksheet No. 1 Solutions

To solve the first problem on the worksheet, set it up as follows: 

Let "P" represent the variable for "puck"

Let "S" represent the variable for "stick"

So, 5P + 3S = $23, and 5P + 1S = $20

Then, subtract one equation from the other (since you know the dollar amounts):

5P + 3S - (5P + S) = $23 - $20. 

5P + 3S - 5P - S = $3. Subtract 5P from each side of the equation, which yields: 2S = $3. Divide each side of the equation by 2, which shows you that S = $1.50

Then, substitute $1.50 for S in the first equation:

5P + 3($1.50) = $23, yielding 5P + $4.50 = $23. You then subtract $4.50 from each side of the equation, yielding: 5P = $18.50.

Divide each side of the equation by 5 to yield:

P = $3.70

Note that the answer to the first problem on the answer sheet is incorrect.  It should be $3.70 . The other answers on the solution sheet are correct.

Worksheet No. 2

Print PDF : Worksheet No. 2

To solve the first equation on the worksheet, students will need to know the equation for a rectangular prism (V = lwh, where "V" equals volume, "l" equals the length, "w" equals the width, and "h" equals the height). The problem reads as follows:

"Excavation for a pool is being done in your backyard. It measures 42F x 29F x 8F. The dirt will be taken away in a truck that holds 4.53 cubic feet How many truckloads of dirt will be taken away?"

Worksheet No. 2 Solutions

Deb Russell

Print PDF : Worksheet No. 2 Solutions

To solve the problem, first, calculate the total volume of the pool. Using the formula for the volume of a rectangular prism (V = lwh), you would have:

V = 42F x 29F x 8F = 9,744 cubic feet

Then, divide 9,744 by 4.53, or:

9,744 cubic feet ÷ 4.53 cubic feet (per tuckload) = 2,151 truckloads

You can even lighten up the atmosphere of your class by exclaiming: "You are going to have to use quite a few truckloads to build that pool."

Note that the answer on the solution sheet for this problem is incorrect. It should be 2,151 cubic feet. The rest of the answers on the solution sheet are correct.

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Grade 8 Algebra Word Problems

These lessons cover some examples and solutions for algebra word problems that you will commonly encounter in grade 8.

Related Pages More Math Word Problems Algebra Word Problems

How to write algebra word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods?

Grade 8 Algebra Word Problems How to solve algebra word problems using systems of linear equations?

Example: Devon is going to make 3 shelves for her father. He has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?

Grade 8 Algebra Word Problems - Line Segments

Example: If JK = 7x + 9, JL = 114 and KL = 9x + 9. Find KL.

Grade 8 number word problems - common core How to write word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods?

Example 1: The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers?

Example 2: There are 356 Grade 8 students at Euclid’s Middle School. Thirty-four more than four times the number of girls is equal to half the number of boys. How many boys are in Grade 8 at Euclid’s Middle School? How many girls?

Example 3: A family member has some five-dollar bills and one-dollar bills in their wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have?

Example 1: A friend bought 2 boxes of pencils and 8 notebooks for school and it cost him $11. He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would notebooks cost?

• A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his animals and realizes he has a total of 114. How many cows does the farmer have? How many chickens?
• The length of a rectangle is 4 times the width. The perimeter of the rectangle is 45 inches. What is the area of the rectangle?
• The sum of the measures of angles x and y is 127". If the measure of angle x is 34° more than half the measure of angle y, what is the measure of each angle?

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Get ready for 8th grade

Unit 1: get ready for numbers and operations, unit 2: get ready for solving equations and systems of equations, unit 3: get ready for linear equations and functions, unit 4: get ready for geometry.

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How to Master Work Problems: A Comprehensive Step-by-Step Guide

Understanding work problems in mathematics often involves dealing with scenarios where different people (or machines) contribute to completing a task. These problems can be solved by using the formula \(W=R×T\), where \(W\) is Work, \(R\) is Rate, and \(T\) is Time. Here is a step-by-step guide to help you understand and solve these problems:

Step-by-step Guide to Master Work Problems

Step 1: understand the problem.

• Read the Problem Carefully: Identify what the problem is asking. Pay attention to the time taken by each person or machine to complete the work independently.
• Define the Work: Usually, the total work done is considered as \(1\) unit. For example, mowing a lawn, painting a wall, or filling a tank is each considered as 1 unit of work.

Step 2: Determine the Rates

• Calculate Individual Rates: Determine the rate at which each person or machine completes the work. If a person completes the work in \(T\) hours, their rate is \(\frac{1}{T}\)​ units of work per hour.
• Combine Rates for Collaborative Work: If multiple people or machines work together, add their rates. For instance, if Person \(A\) has a rate of \(\frac{​1}{T_{A}}\)​ and Person \(B\) has a rate of \(\frac{1}{T_{B}}\), their combined rate is\(\frac{​1}{T_{A}}+\frac{1}{T_{B}}\) ​.

Step 3: Set Up the Equation

• Use the Work Formula: The formula \(W=R×T\) is pivotal. For combined work, set \(W=1\) and use the combined rate for \(R\).
• Formulate the Equation: The equation usually looks like \(1=(\frac{​1}{T_{A}}+\frac{1}{T_{B}})×T\), where \(T\) is the time taken for the combined work.

Step 4: Solve for the Unknown

• Rearrange the Equation: Isolate the variable you are solving for. This might involve algebraic manipulation.
• Solve Mathematically: Use algebra to find the value of the unknown variable. This might involve finding a common denominator, simplifying fractions, or solving linear equations.

Step 5: Check Your Solution

• Verify the Answer: Plug your answer back into the equation to see if it makes sense. Check if the units and the context align correctly.
• Consider Practical Implications: Ensure that the solution is practical and makes sense in the context of the problem.

Understanding each step and applying it to various problems will enhance your ability to tackle work problems effectively.

Sarah can clean a room in \(2\) hours. When she works with her friend Lisa, they can clean it in \(1.5\) hours. How long would it take Lisa to clean the room alone?

• Sarah’s rate \(=\frac{1}{2}\) room per hour.
• Together, their rate \(=\frac{1}{1.5}​\) room per hour.
• Let Lisa’s time be \(T\) hours, so her rate \(=\frac{1}{T}\)​.

Combine the rates: \(\frac{1}{2}+\frac{1}{T}=\frac{1}{1.5}​\)

Solve for \(T\): \(\frac{1}{T}=\frac{2}{3}-\frac{1}{2}=\frac{4-3}{6}=\frac{1}{6}\)​ So, \(T=6\) hours.

Kevin can type a document in \(5\) hours. Working together with Rachel, they can type it in \(4\) hours. How long would it take Rachel alone?

• Kevin’s rate \(=\frac{1}{5}\)​ document per hour.
• Together, their rate \(=\frac{1}{4}\) document per hour.
• Rachel’s rate \(=\frac{1}{T}\)​.

Combine the rates: \(\frac{1}{5}+\frac{1}{T}=\frac{1}{4}​\)

Solve for \(T\): \(\frac{1}{T}=\frac{1}{4}-\frac{1}{5}=\frac{5-4}{20}=\frac{1}{20}\)​ So, \(T=20\) hours.

by: Effortless Math Team about 6 months ago (category: Articles )

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M-STEP Grade 6 Math for Beginners The Ultimate Step by Step Guide to Preparing for the M-STEP Math Test

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Build Confidence with Math Problem Solving

Daily Problem Solving will help your 8th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .

What you'll get with this download:

Your download includes a full week of Daily Problem Solving for Grade 8 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.

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8th Grade Math Worksheets

First things first, prioritize major topics with our printable compilation of 8th grade math worksheets with answer keys. Pursue conceptual understanding of topics like number systems, expressions and equations, work with radicals and exponents, solve linear equations and inequalities, evaluate and compare functions, understand similarity and congruence, know and apply the Pythagorean Theorem, find volume and surface area, develop an understanding of statistics and probability and much more. Our free math worksheets for grade 8 students make sure they start right!

Select Grade 8 Math Worksheets by Topic

Explore 2,400+ Eighth Grade Math Worksheets

Converting Fractions to Decimal

Convert each fraction with a multiple of 10 as its denominator into a decimal number by placing the decimal point at the right spot.

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Finding the Square Roots of Perfect Squares

Apply prime factorization and determine the square roots of the first fifty perfect squares offered as positive integers.

Slope of a Line passing through Two Points

Use the formula, m = (y 2 - y 1 ) / (x 1 - x 1 ) to find the slope(m) of a line passing through two points: (x 1 ,y 1 ) and (x 2 ,y 2 ).

Solving Multi-Step Equations

Follow the order of operations, rearrange to make the unknown variable the subject, and solve for its integer value.

Identifying Functions from Ordered Pairs

Observe each set of ordered pairs given in Part A, figure out ordered pairs from graphs in Part B, and state if they represent a function.

Translation on Graphs | Writing Coordinates

Slide each figure in the said direction: up or down, left or right. Write the coordinates of the shifted image.

Congruence | Congruent Parts

Complete the congruence statement for each pair of triangles by writing the corresponding side or corresponding angle.

Finding the Interior Angle

Find the measure of the indicated interior angle by subtracting the sum of the known angles from 180.

Interior Angles - Finding the Unknown

Observe whether the interior angles lie on the same side or opposite sides of the transversal and find the unknown angle.

Identifying Right Triangles

Square the adjacent and opposite sides of the triangle; take the root of their sum; if you arrive at the hypotenuse, then it's a right triangle.

Volume of Cones

Plug the given radius(r) and height(h) in the formula V = 1/3πr 2 h and find the volume of the cone.

Mean, Median, Mode, and Range

Read each word problem with a real-life scenario and find the mean, median, mode, and range for each data set.

Converting Fractions to Percent

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Convert to the Standard Form

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Free Printable Addition Word Problems Worksheets for 8th Grade

Addition Word Problems: Discover a collection of free printable worksheets for Grade 8 math teachers, featuring math addition word problems to enhance students' problem-solving skills and understanding.

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Explore printable Addition Word Problems worksheets for 8th Grade

Addition Word Problems worksheets for Grade 8 are an essential resource for teachers looking to help their students excel in math. These worksheets provide a variety of math word problems specifically designed for Grade 8 students, covering a wide range of topics and difficulty levels. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are not only learning the necessary mathematical concepts but also developing crucial problem-solving skills. The use of real-life scenarios in these math word problems helps students to better understand the practical applications of addition, making the learning process more engaging and effective. With a comprehensive collection of Addition Word Problems worksheets for Grade 8, teachers can easily tailor their instruction to meet the diverse needs of their students and help them achieve success in math.

Quizizz is an excellent platform that offers a variety of resources, including Addition Word Problems worksheets for Grade 8, to support teachers in their quest to provide engaging and effective math instruction. In addition to worksheets, Quizizz also offers interactive quizzes, games, and other learning tools that can be easily integrated into the classroom. These resources are designed to help students not only master the mathematical concepts but also develop a love for learning and a deeper understanding of the subject matter. Teachers can easily track their students' progress and identify areas where additional support may be needed. By utilizing Quizizz in conjunction with Addition Word Problems worksheets for Grade 8, teachers can create a dynamic and interactive learning environment that fosters both academic growth and a love for math.