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

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09 Oct 2013, 19:23

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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?

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

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10 Oct 2013, 04:39

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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

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

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11 Feb 2015, 15:16

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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.

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

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15 Feb 2016, 19:18

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

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17 Jul 2016, 12:48

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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20 Jul 2017, 08:29

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

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22 Jul 2017, 19:03

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.

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

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07 Aug 2017, 09:27

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

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