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Six machines at a certain factory operate at the same constant rate.

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Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post Updated on: 18 Jun 2016, 01:42
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Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24

Originally posted by tanad on 17 Jun 2016, 14:12.
Last edited by Bunuel on 18 Jun 2016, 01:42, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post Updated on: 17 Jun 2016, 16:04
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Suppose each machine finishes a job in x hours. This would mean that each machine has a rate of \(\frac{1}{x}\) jobs/hour. Using the equation R*T=Work, we can figure out the rest.

We know that four machines combined would work four times as fast as just one machine working alone. Thus, the combined rate of 4 machines is \(\frac{4}{x}\). Furthmore the time it takes to complete the order is 27 hours. Now we can put the complete order in terms of x:

\(R * T = Work\)
\(\frac{4}{x} * 27 = Work\)
\(Work = \frac{4*27}{x}\)

Note that I didn't do out the actual multiplication. There's no time on the actual GMAT!

Next, let's look at 6 machines. Working together, they have a rate of \(\frac{6}{x}\). From before, we know the order size is \(\frac{4*27}{x}\). We need to figure out the new time.

\(\frac{6}{x} * T = \frac{4*27}{x}\)
\(T = \frac{4}{6}*27 = \frac{2}{3}*27 = 18\) (**Note that the x's cancel)

Thus, the difference is 27-18 = 9 hours, which is answer choice A.

Originally posted by bbear on 17 Jun 2016, 14:31.
Last edited by bbear on 17 Jun 2016, 16:04, edited 1 time in total.
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 17 Jun 2016, 15:50
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6t=4*27
t=18 hours
27-18=9 fewer hours
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 17 Jun 2016, 23:37
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tanad wrote:
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24


Total work = 27 * 4

Time taken when 6 machines work = \(\frac{(27*4)}{6}\) => 18 hours

So, working together 6 machines take 9 hours less ( 27 - 18 )

Answer will be (A)

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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 18 Jun 2016, 01:43
tanad wrote:
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24


This is a copy of the following OG question: five-machines-at-a-certain-factory-operate-at-the-same-constant-rate-219084.html
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 18 Jun 2016, 03:08
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tanad wrote:
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24


Time taken by 4 machines to fill a certain production order = 27 hours
Time taken by 1 machine to fill that production order = 27 * 4 = 108 hours
Time taken by 6 machines to fill that production order = 108/6 = 18 hours

Number of fewer hours it takes 6 machines to fill that production order = 27 - 18 = 9 hours
Answer A
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 19 Jun 2016, 03:44
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given 4 machines can complete the job in 27 hrs,
--> rate of 4 machines = 1/27
--> rate of each machine = (1/27)/4
--> rate of 6 machines = 6 * ( (1/27)/4 )= 1/18
hence , time taken by 6 machines = 18 hrs
difference = 27 - 18 = 9
option A
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 20 Jul 2016, 09:34
Abhishek009 wrote:
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?

A: 9
B: 12
C: 16
D: 18
E: 24

Total work = 27 * 4

Time taken when 6 machines work = \(\frac{(27*4)}{6}\) => 18 hours

So, working together 6 machines take 9 hours less ( 27 - 18 )

Answer will be (A)


Quote:

Bunuel Sir and Abhishek Sir,
Please tell me if my approach is wrong.

Let "r" be the rate of the machine.

Rate * Time = Workdone
So,

4 r * 27 = 6 r *X

>>> X = 4*27/6
>>> X = 18

How many fewer hours does it take = 27 -18 = 9

Please let me know.
Thanks again!

Regards,
Yosita

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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 20 Jul 2016, 11:11
1/(4*27)=1/108=rate of 1 machine
let t=time
t*6*(1/108)=1
t=18
27-18=9
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Re: Six machines at a certain factory operate at the same constant rate.  [#permalink]

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New post 24 Oct 2018, 07:56
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Re: Six machines at a certain factory operate at the same constant rate. &nbs [#permalink] 24 Oct 2018, 07:56
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