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

1. ## 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!

2. 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 $\displaystyle \frac W8$ per hour and the second person is doing $\displaystyle \frac W{12}$ 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:

$\displaystyle \frac W8 (t-2) + \frac W{12} t = W$

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

$\displaystyle \frac5{24} t = \frac 54~\implies~\boxed{t = 6\ h}$

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