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Working alone at their respective constant rates, machine \(A\) and machine \(B\) can fill a certain order in \(3\) hour

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Working alone at their respective constant rates, machine \(A\) and machine \(B\) can fill a certain order in \(3\) hour

by Vincen » Fri Jul 09, 2021 11:16 am

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Working alone at their respective constant rates, machine \(A\) and machine \(B\) can fill a certain order in \(3\) hours and \(6\) hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill \(\dfrac12\) of that order?

A: \(\dfrac12\)

B: \(\dfrac34\)

C: \(1\)

D: \(1 \frac14\)

E: \(1 \frac12\)

Answer: C

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Re: Working alone at their respective constant rates, machine \(A\) and machine \(B\) can fill a certain order in \(3\)

by Brent@GMATPrepNow » Sun Jul 11, 2021 5:35 am
Vincen wrote: ↑
Fri Jul 09, 2021 11:16 am
 Working alone at their respective constant rates, machine \(A\) and machine \(B\) can fill a certain order in \(3\) hours and \(6\) hours, respectively. If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill \(\dfrac12\) of that order?

A: \(\dfrac12\)

B: \(\dfrac34\)

C: \(1\)

D: \(1 \frac14\)

E: \(1 \frac12\)

Answer: C

Source: GMAT Prep
One approach is to assign a "nice value" to the job.
That is, a value that works well with the given information of 3 hours and 6 hours
So let's say the order consists of making 18 widgets

Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively
In other words, Machine A can make 18 widgets in 3 hours, which means Machine A's RATE = 6 widgets per hour
This also tells us that Machine B can make 18 widgets in 6 hours, which means Machine B's RATE = 3 widgets per hour

If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?
COMBINED rate = 6 + 3 = 9 widgets per hour

We want to fill 1/2 the order.
1/2 of 18 widgets is 9 widgets
So we want to make 9 widgets

time = output/rate
So, time = 9/9 = 1 hour

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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