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If 6 identical machines, each working at the same uniform constant

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pintukr
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If 6 identical machines, each working at the same uniform constant [#permalink] New post   29 Aug 2023, 16:48
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If 6 identical machines, each working at the same uniform constant rate, can complete a job working together in 3 hours, how long (in minutes) will it take 9 of these machines, working at their constant rate, to complete 1/3 of this job?

A. 60
B. 45
C. 40
D. 30
E. 24
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Re: If 6 identical machines, each working at the same uniform constant [#permalink] New post   29 Aug 2023, 19:21
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Total machine Hours for job = 6 * 3 = 18 hours
For 1/3 rd of job = 18 * 1/3 = 6 hours
Nine machines will complete 1/3 rd of job in = 6 * 1/9 * 60 = 40 minutes

Answer(c)

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Re: If 6 identical machines, each working at the same uniform constant [#permalink] New post   31 Aug 2023, 06:45
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Rate of each machine = 1/x
6/x = 1/3
1/x = 1/18

T is time in hrs,

T* 9/x = 1/3
T* 9* 1/18 = 1/3
T = 2/3 hrs = (2/3)*60 mins = 40 mins

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GmatKnightTutor
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If 6 identical machines, each working at the same uniform constant [#permalink] New post   14 Oct 2023, 07:16
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MORE machines should take LESS time to do the same job. It's an inverse relationship.

6 people = 3 hours
9 people = x hours

Multiply HORIZONTALLY since it's an inverse relationship.

18 = 9x

x is equal to 2

Basically, it would take 9 machines a total of 2 hours to do the whole job.

However, we're asked to find out how long it would take 9 machines to do 1/3 of the job. Less work takes less time so this is NOT an inverse situation. You can simply find out what a third of 2 hours is: 40 minutes.

(C) is your answer.

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If 6 identical machines, each working at the same uniform constant [#permalink]
14 Oct 2023, 07:16

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