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Videos, worksheets, solutions, and activities to help Algebra students learn about work problems.

Work Problem 3

This video focuses on a problem of the type: Worker A can do a job in x hours, and worker B can do a job in y hours. How fast can worker A and B do a job if they work together?

Example: Mary takes 10 minutes to vacuum a room, but Beth takes 15 minutes. How long will it take to vacuum the room if they work together?

Barry can mow the lawn in 55 minutes. If his son helps him, it gets done in 30 minutes. How long would it take his son to mow the lawn if he worked alone?

The equation used is:

rate × time = amount of work done

Example: If Joe can paint a house in 6 hours and Sam can paint the same house in 8 hours, how long does it take them to do it working together?

If it takes you 7 hours to paint a house then the rate is 1/7 per hour.

In general, if it takes somebody x hours to do something then the rate is 1/x per hour.

Example: It takes an experienced painter 6 days to paint a house. It takes an apprentice 8 days to paint the same house. How long would it take if they worked together?

Step 1: Name what x is.

Step 2: Define everything else in the problem in terms of x.

Step 3: Write the equation.

Step 4: Solve the equation.

Step 5: Answer the question.

Example: One pipe can fill a tank in 8 hours. Another pipe empty the tank in twelve hours. If both pipes are opened simultaneously, how long will it take to fill the tank?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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