It would take one machine \(4\) hours to complete a large production order and another machine \(3\) hours to complete

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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) \(7\)

Answer: C

Source: Official Guide

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Vincen wrote:
Wed Oct 06, 2021 6:39 am
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) \(7\)

Answer: C

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
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