Thread: A "work" word problem, need help!

This problem is driving me nuts, help would be greatly appreciated.


"One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

Any ideas? thanks!

Originally Posted by itokai

This problem is driving me nuts, help would be greatly appreciated.


"One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together?"


If they worked at the same time, i know the answer is just under 5 hours total...but the first person has to work 2 hours less, and i dont know how to insert that in.

Any ideas? thanks!

Let W denote the total amount of work which should be done. Then the first person is doing per hour and the second person is doing per hour.

Let t denote the working time (in hours!) of the second person. Then the first person works only (t - 2) hours. Therefore the complete work is done:



Divide by W, expand the brackets and collect like terms:



Since your question asks "...how many hours will it take them working together?" the answer is 4 hours.