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If 6 machines run at the same constant rate, they can [#permalink]

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05 Nov 2010, 12:47

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If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

6 machines can do a job in 8 hrs. 5 machines con do a job in ?

Now think, will 5 machines take more than 8 hrs, or less? Of course more than 8 hrs since fewer machines are working.

So number of hours 5 machines will take = \(8 * (\frac{6}{5})\)

Basically, you need hours so given hours term i.e. \(8 * \frac{6 machines}{5 machines}\) to get 9.6 hours.

We multiply by 6/5 to increase 8 since more hours are required. It is actually a Variation question (Inverse Variation here) but it is just easier to think in terms of more/less.

Another e.g. 10 people make 5 chairs in a day. How many people do we need to make 12 chairs. Simply multiply 10 (the number that you want to change) by 12/5 because you want to increase the number of people to make more chairs: \(10 * (\frac{12}{5}) = 24\) people

Yet another e.g. 10 people need 4 hours to complete a job. How many hours do 18 people need to complete the same job? \(4 * (\frac{10}{18})\) = 2.2 hrs If there are more people, they will need fewer hours so multiply by 10/18 (not 18/10).
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If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

A. 38 B. 72 C. 80 D. 90 E. 96

The question can be answered in 30 sec if you have a fundamental understanding of simple principle: Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

Six machines can do 1/8 of the job within an hour. => 1 machine can do 1/48 of the job within a hour. => 5 machines can do 5/48 of the job within a hour.

=> 5 machines can do a full job in 48/5 hours.

The difference between 48/5 hours and 5 hours is 8/5, which is 96 minutes (the answer to the question).

Re: If 6 machines run at the same constant rate, they can [#permalink]

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26 Feb 2012, 07:56

rtaha2412 wrote:

If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

A. 38 B. 72 C. 80 D. 90 E. 96

On the same lines as Bunuel. The new rate is 5/6 of the earlier. The new total time will be 6/5 of original. To get the extra time 6/5 - 1 = 1/5. It will take 1/5 (20%) of original time to complete the same task. 1/5 * 480 = 96mins

Re: If 6 machines run at the same constant rate, they can [#permalink]

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15 Nov 2012, 00:40

Setup the rate equation for 6 machines working for 8 hours to finish a job: \((\frac{1}{m}+\frac{1}{m}+\frac{1}{m}+\frac{1}{m}+\frac{1}{m}+\frac{1}{m})(8hours)=1==>m=48hours\)

Setup the rate equation for 5 machines to finish the same job: \(\frac{5}{48}t=1==>t=\frac{48}{5}=9.6hours\)

Re: If 6 machines run at the same constant rate, they can [#permalink]

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31 Jan 2015, 11:59

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Re: If 6 machines run at the same constant rate, they can [#permalink]

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20 Feb 2015, 09:23

rtaha2412 wrote:

If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

Re: If 6 machines run at the same constant rate, they can [#permalink]

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23 Jun 2016, 10:42

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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