Work Rate Problem
Free interactive math game: Work Rate Problem — Together, how long?. Part of the Units & Time category on MathKite.
Example problems
Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.
- Finn can paint a room in 6 hours. Emma can paint the same room in 12 hours. How long will it take them working together?
- Emma can paint a room in 8 hours. Dana can paint the same room in 8 hours. How long will it take them working together?
- Finn can paint a room in 12 hours. Chris can paint the same room in 4 hours. How long will it take them working together?
- Bob can paint a room in 10 hours. Emma can paint the same room in 15 hours. How long will it take them working together?
About this exercise
How long a job takes when several people share it.
How to solve it
Turn each worker into a rate of jobs per hour, add the rates, then divide one job by the combined rate.
Worked example
Two people who each finish in 6 hours work at one sixth each, so one third together, finishing in 3 hours.
Common mistake
Averaging the times. Two six-hour workers together take three hours, not six.