Work Word Problem

[ENHSmath]

It takes Sam 12 hours to scrape the paint from a fence, but Harold can do the job in 9 hours. How long does Sam work alone before being joined by Harold if they finished the job working 3 hours together?

Answer: 5.00

[Shawn]

It is basically a rate problem.

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Think of it as a rate problem, where they need to get 1 "project" done. Harold is going to work 3 hours getting 1/9 of the project done each hour. Sam is then going to work these 3 hours plus an unknown time x hours at a rate of 1/12 of the project an hour. So Harold is going to do 3*1/9 and Sam is going to do 3*1/12 in the 3 hours and x*1/12 in the x hours or (3+x)*(1/12) in the full 3+x hours. So you get the formula above. If you have any questions or don't understand the solution, let me know. Feel free to post any questions, and I will do my best.

-Shawn