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Two machines, Y and Z, work at constant rates producing identical item

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Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 May 2016, 11:51, edited 1 time in total.
Renamed the topic and edited the question.

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umg4147 wrote:
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2


Machine Z is 1.5 times slower than machine Y. So, if machine Y takes 9 minutes to produce a batch of items, then it takes machine Z 9*1.5 = 13.5 minutes to produce the same number of items.

Answer: E.
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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink]

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New post 16 May 2016, 13:36
Hey awsome bunuel, i went a bit long in deducing the actual relation between the Rates.

Now atleast i know what to think when i see such question and dont need to go on the practice pad .

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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink]

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New post 14 Jun 2016, 13:35
lf you assume that machine Y produces 3 items per minute then machine Z produces 2 items per minute. If machine Y takes 9 minutes to produce a batch of items, then machine Y produces 27 items in these 9 minutes. Since machine Z produces the same number of items, it should take machine Z 13.5 minutes to produce 27 items.

At times, it just helps to plug in numbers...

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Two machines, Y and Z, work at constant rates producing identical item [#permalink]

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rate z/rate y=2/3
time z/time y=3/2
3/2*9=13 1/2 minutes

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Re: Two machines, Y and Z, work at constant rates producing identical item [#permalink]

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Re: Two machines, Y and Z, work at constant rates producing identical item   [#permalink] 05 Sep 2017, 08:24
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