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Work problems have direct real-life applications. We often need to determine how many people are needed to complete a task within a given time. Alternatively, given a limited number of workers, we often need to determine how long it takes to finish a project. Here we deal with the basic math concepts of how to handle these types of problems.

In these lessons, 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

Related Topics:

Math Work Problems

More Algebra Word Problems

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 2:

It takes Maria 10 hours to pick forty bushels of apples. Kayla can pick the same amount in 12 hours.
How long will it take if they work together? Round your answer to the nearest hundredths.

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 2:

Jim can dig a hole by himself in 12 hours.
John can do it in 8 hours and Jack can do it in 6.
How long will it take if they work together?

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.

Example 2:

Pipe 1 takes 5 days to drain a pool and pipe 2 takes 7 days to drain the pool.
How long will it take for the two pipes to drain the pool together?

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 by 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:

Latisha and Ricky work for a computer software company. Together they can write a particular computer program in 19 hours. Latisha can write the program by herself in 32 hours. How long will it take Ricky to write the program alone?

Example:

A swimming pool is being drained through the drain at the bottom of the pool, and filled by the hose at the top. If the hose can fill the pool in 21 hours and the drain can empty the pool in 24 hours, how many hours will it take to fill the pool if the drain is left open? Express the answer in hours and round the answer to the nearest hour if needed.