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

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Oct 06, 2021 6:39 am

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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

Source: Beat The GMAT — Problem Solving | Wed Oct 06, 2021 6:39 am

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Re: It would take one machine $4$ hours to complete a large production order and another machine $3$ hours to comple

by Brent@GMATPrepNow » Wed Oct 06, 2021 12:00 pm

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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