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Machine X, working alone at a constant rate, produces w widgets in 15

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harishsridharan
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Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   Updated on: 02 Apr 2021, 01:23
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Machine X, working alone at a constant rate, produces w widgets in 15 minutes. Machine Y, working alone at a constant rate, takes twice as much time to produce w widgets. How long, working simultaneously at their respective rates, would it take both machines working together to complete 4w widgets?


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40

Originally posted by harishsridharan on 01 Apr 2021, 21:56.
Last edited by harishsridharan on 02 Apr 2021, 01:23, edited 4 times in total.
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Re: Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   02 Apr 2021, 00:10
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The correct answer is 40, which is not given in the answer choice.

I found this question, along with the correct answer on Manhattan GRE Prep Blog.
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Re: Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   02 Apr 2021, 00:15
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Also the problem is to show and explain the concept of work/rate

It does not provide any answer choices
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Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   02 Apr 2021, 01:28
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Carcass wrote:
Also the problem is to show and explain the concept of work/rate

It does not provide any answer choices


Corrected sir!
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Re: Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   02 Apr 2021, 03:40
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Thank you Sir
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Re: Machine X, working alone at a constant rate, produces w widgets in 15 [#permalink] New post   02 Apr 2021, 06:09
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harishsridharan wrote:
Machine X, working alone at a constant rate, produces w widgets in 15 minutes. Machine Y, working alone at a constant rate, takes twice as much time to produce w widgets. How long, working simultaneously at their respective rates, would it take both machines working together to complete 4w widgets?


Show: :: OA
40


Concept: If X can do a piece of job in \(A\) minutes while Y and can do the same job in \(B\) minutes, working together they can finish the job in \(\frac{AB}{(A + B)}\) minutes.

So, both machines can make \(w\) widgets in \(\frac{(15)(30)}{(15 + 30)} = 10\) minutes
Therefore, \(4w\) widgets can be made in \((4)(10) = 40\) minutes
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