Question

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?A. 6B. 9C. 12D. 27E. 48

Answer 1

Option B is the answer.

Explanation:

Given is that all 3 machine works at same rate or
`(1)/(x)`

We get;
`(1)/(x) +(1)/(x) +(1)/(x) =(1)/(36)`

=>
`(3)/(x) =(1)/(36)`

x = 108

Now given is that the fourth machine was used with same rate that is
`(1)/(x)`

Total rate for 4 machines =
`(4)/(x)`

=
`(4)/(108)`

=
`(1)/(27)`

This is the over all rate of four machines.

And we know that time = 1/Rate

So, time = 27 hours

Therefore, the fewer hours were
`36-27=9` hours

Option B is the answer.