A carpenter is working on a deck. He hires two assistants who work 60% as fast as he works. If all three work together on the deck, they should finish in what fraction of the time that he would take working alone?
+128474 Call the number of hours it takes the carpenter to finish the job = x
So......the fraction of the job that he can finish in one hour is 1/x
So.....the fraction of the job that of the other two can do in one hour = .60 (1/x)
So....the total fraction of work done in one hour by all three working together is
1/ x + .60 (1/x) + .60 (1/x) = (1 + .60 + .60) / x = (2.2) / x
So....the total time they take is the reciprocal of this = x / (2.2)
So....the fration of the time that they would take working together compared to the carpenter working alone is
( x/ 2.2) / x =
(x /2.2) * (1/x) = 1 / 2.2 = 10/22 = 5/11 of the time
