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Working simultaneously at an identical constant rate,

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by VJesus12 » Thu Nov 30, 2017 10:04 am
Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48

The OA is D .

I am confused here. Can any experts clarify this PS question to me?
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by [email protected] » Thu Nov 30, 2017 10:44 am
Hi VJesus12,

We're told that - working simultaneously at an identical constant rate - it takes 6 machines 8 hours to produce Y widgets. We're asked for the number of machines, working at that identical constant rate, are necessary to produce 2Y widgets in 4 hours.

With these types of Work questions, it helps to determine the total amount of work needed to complete a task.

(6 machines)(8 hours each) = 48 machine-hours of work to produce Y widgets.

The question asks us to create 2Y widgets, which is DOUBLE the number of widgets (above). Thus, it would take DOUBLE the work (re: 96 machine-hours of work). With just 4 hours to total time, we would need....

(X machines)(4 hours each) = 96 machine-hours of work to produce 2Y widgets.
X = 24 machines

Final Answer: D

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by Jeff@TargetTestPrep » Tue Jan 02, 2018 11:04 am
VJesus12 wrote:Working simultaneously at an identical constant rate, it takes 6 machines 8 hours to produce y widgets. How many machines, working at that identical constant rate, are necessary to produce 2y widgets in 4 hours?

A. 6
B. 12
C. 18
D. 24
E. 48

We are given that the rate of 6 machines is y/8. Using a proportion, we can determine how many machines work at a rate of 2y/4 = y/2.

6/(y/8) = n/(y/2)

48/y = 2n/y

48y = 2ny

24 = n

Alternate solution:

We see that the number of widgets needed to be produced (2y) is twice the given number of widgets (y). Thus, we need to double 6 machines to 12 machines so that in 8 hours they can produce 2y widgets. However, we see we need to produce these 2y widgets in 4 hours, which is half of the given 8 hours. Thus, we need to double the machines again from 12 machines to 24 machines to produce 2y widgets in 4 hours.

Answer: D

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