In these lessons, we will learn how to solve work problems that involve more than two persons. Look at the related pages above for work problems in other situations.
Work Problems are word problems that involve different people doing work together but at different rates. If the people were working at the same rate then we would use the Inversely Proportional Method instead.
The formula for “Work” Problems that involve three persons is:
This formula can be modified for two or more persons. It can also be used in problems that involve pipes filling up a tank.
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?
Step 1: Assign variables:
Let x = time taken by Peter
Step 2: Use the formula:
Step 3: Solve the equation
Multiply both sides with 30x
Answer: The time taken for Peter to paint the fence alone is
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.
Jim can dig a hole by himself in 12 hours. John can do it in 8 hours. Jack can do it in 6. How long will it take them if they all work together?
If Amy, Bianca and Carrie work together on a job, it will take one and one-third hours. If only Amy and Bianca work, it would take one and five-sevenths hours, but if Bianca and Carrie work, it would take two and two-fifths hours, how long would it take each girl working alone to complete the job?
John can paint a garage in 8 hours. Gary can do it in 6 hours. Fred can do it in 4 hours. How long will it take if they all paint together?
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