2014-06-18 09:00:10

Two different students, Alex and Benny, working together can complete a project in 6 hours. Working alone, Alex can do the job in 10 hours. How many hours will it take Benny to do the job alone?

(A) 2.5 hours
(B)  4 hours
(C) 10 hours
(D) 12 hours
(E) 15 hours

The correct answer is E
Explanation: Start by figuring out how much of the job Alex is doing. Since it takes Alex 10 hours alone and 6 hours with Benny, Alex is doing 60% of the job (that is, in 6 hours, Alex will have done 60% of the total job). Benny must be responsible for the remaining 40% of the job, meaning that 6 hours must be the amount of time it takes him to do 40% of the job. Set up a proportion:

100%    =               40%
x hours                  6 hours

Cross multiply: 100% of 6 = 40% of x, so 6 = .4x. Divide both sides by .4 to get x = 15.