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?

Guest Jan 11, 2021

#1**+2 **

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

CPhill Jan 11, 2021