In this lesson, we will learn

- how to solve work problems that involve two persons
- how to solve work problems that involve more than two persons
- how to solve work problems that involve pipes filling up a tank

The formula for “Work” Problems that involve two persons is

This formula can be extended for more than two persons. It can also be used in problems that involve pipes filling up a tank.

Example 1:

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

Solution:

Step 1: Assign variables:

Let

x= time to mow lawn together

Step 2: Use the formula:

Step 3: Solve the equation

The LCM of 40 and 60 is 120

Multiply both sides with 120

Answer: The time taken for both of them to mow the lawn together is 24 minutes.

Example 1:

Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?

Solution:

Step 1: Assign variables:

Let

x= time taken by Peter

Step 2: Use the formula:

Step 3: Solve the equation

Multiply both sides with 30

x

Answer: The time taken for Peter to paint the fence alone is hours.

Example 1:

A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?

Solution:

Step 1: Assign variables:

Let

x= time taken to fill up the tank

Step 2: Use the formula:

Since pipe C drains the water it is subtracted.

Step 3: Solve the equation

The LCM of 3, 4 and 5 is 60

Multiply both sides with 60

Answer: The time taken to fill the tank is hours.

It is possible to solve word problems when two people are doing a work job together by solving systems of equations. To solve a work word problem, multiply the hourly rate of the two people working together times the time spent working to get the total amount of time spent on the job. Knowledge of solving systems of equations is necessary to solve these types of problems.

Example: Drew can paint a room in 3 hours. It takes Brad, his artistic brother, 8 hours to paint a room of the same size. How long will it take Brad and Drew to paint a room together assuming no gain or loss of efficiency? (Round up to the nearest minute)

Example: Working with your cousin, you can split a cord of firewood in 5 hours. Working alone, your cousin can complete the job in 7 hours. How long would it take you to split the firewood working alone? (Round up to the nearest minute)

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