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Three machines operating independently, simultaneously, and

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Three machines operating independently, simultaneously, and [#permalink]

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Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48
[Reveal] Spoiler: OA
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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 10 Oct 2013, 00:33
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If 3 Machines can do the work in 36 hr then 4 Machines can do the work in 3/4*36 = 27 Hrs. hence time saved will be 9hr

option B is the correct answer
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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 10 Oct 2013, 03:39
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Hi,

all 3 machine works at same rate = 1/x

1/x + 1/x + 1/x = 1/36
3/x = 1/36
x = 108.

Fourth machine was used with same rate (1/x)
Total Rate for 4 MAchines
= 4/x
=4/108
=1/27 is the over all rate of four machine
So time is 1/Rate = 27 hrs

Question asked was "how many fewer hours of simultaneous operation could the production order be fulfilled"
so 36 - 27 = 9 Hrs
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Re: Three machines operating independently, simultaneously, and [#permalink]

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3 Machines 36 hr
1 Machines 108 hrs
4 machines 27 hrs

Now 36-27=9 hrs fewer......B

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Re: Three machines operating independently, simultaneously, and [#permalink]

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3 -> 36
4 -> x
Because they are inversely related, 4x = 3*36 => x = 27.
36-9 = 27.
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Re: Three machines operating independently, simultaneously, and [#permalink]

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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 12 Feb 2015, 11:55
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Hi All,

These type of "work" questions can be solved in a variety of ways (depending on how you want to do the math).

Since we have 3 machines, each of which works for 36 hours to complete a job, we know that....

(3 machines)(36 hours each) = 108 machine-hours are needed to complete the job.

Since we're told that all the machines work at the same rate, adding a 4th machine is not going to be difficult to deal with. The 108 machine-hours are still needed to complete the job, but now we have 4 machines doing work instead of 3...

(108 machine-hours)/(4 machines) = 27 hours.

Since the original time was 36 hours and the "new" time is 27 hours, the difference is 9 hours.

Final Answer:
[Reveal] Spoiler:
B


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Re: Three machines operating independently, simultaneously, and [#permalink]

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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 17 Jul 2016, 11:48
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48


\(\frac{36}{3}=\) 12 hours (each machine take 12 hours)
(3 machines * 12 hours) = (4 machines take x hours)
12 * 3 = 4 * X
36 = 4x
9 = x
4 machines will take 9 hours less to finish the same order
Answer B
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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 20 Jul 2017, 07:29
Hello from the GMAT Club BumpBot!

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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 22 Jul 2017, 18:03
kiseki wrote:
Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48


Let C = the rate of one of the machines

3C = 1/36
C = 1/(36*3)

Add one more machine to determine the net impact...

4C = 4/(36*3) = 1/(9+3)

It would take 4 machines 27 hours to finish the job.

36-27 = 9 hours.
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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 07 Aug 2017, 08:27
Use inverse proportion concept to solve it quickly.

Initial number of machines=3
New Number of machines=4(after adding one more machine)

So number of machines increases by 1/3 of the initial number

Since time taken will be inversely proportional to the number of machines, therefore if number of machines increases by 1/3, time taken decrease by 1/4

1/4 of 36 = 9.

Therefore B
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Re: Three machines operating independently, simultaneously, and [#permalink]

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New post 07 Aug 2017, 11:10
a usual approach for work rate problems

3 machines, same productivity rate do some work in 36 hours, so mount of work is 108
if 1 more machine with the same rate is added then:

108 = 4*x
x = 27
Question asks "how many fewer hours" so we subtract 27 from initial 36 = 9
Re: Three machines operating independently, simultaneously, and   [#permalink] 07 Aug 2017, 11:10
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