## 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

by Vincen » Wed Oct 06, 2021 6:39 am

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## Global Stats

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) $$7$$

Source: Official Guide

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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 [email protected] » 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) $$7$$

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