It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same

[Vincen]

It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?


(A) \(\dfrac7{12}\)

(B) \(1\frac12\)

(C) \(1\frac57\)

(D) \(3\frac12\)

(E) \(7\)

[spoiler]OA=C[/spoiler]

Source: Official Guide

[Brent@GMATPrepNow]

It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?


(A) \(\dfrac7{12}\)

(B) \(1\frac12\)

(C) \(1\frac57\)

(D) \(3\frac12\)

(E) \(7\)

[spoiler]OA=C[/spoiler]

Source: Official Guide

Another approach is to assign the ENTIRE job a certain number of units.
The least common multiple of 4 and 3 is 12.
So, let's say the ENTIRE production order consists of 12 widgets.

It would take one machine 4 hours to complete a large production...
Rate = output/time
So, this machine's rate = 12/4 = 3 widgets per hour

...and another machine 3 hours to complete the same order.
Rate = units/time
So, this machine's rate = 12/3 = 4 widgets per hour

So, their COMBINED rate = 3 + 4 = 7 widgets per hour.

Working simultaneously at their respective constant rates, to complete the order?
Time = output/rate
= 12/7 hours

Answer: C