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Six machines, each working at the same constant rate

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Six machines, each working at the same constant rate [#permalink]

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Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8
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New post 05 Feb 2012, 23:54
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6 machines in 12 hours can make 6*12=72 units.
x machines in 8 hours can make x*8=72 units x=9

12-9=3 more machines are needed
hope it helps
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Welcome to GMAT Club. Below is a solution for the question. Hope it helps

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
A. 2
B. 3
C. 4
D. 6
E. 8

Let \(x\) be the time needed for 1 machine to complete the job, so rate of one machine is \(\frac{1}{x}\) (rate is the reciprocal of time) --> rate of 6 machines would be \(\frac{6}{x}\).

As \(job=time*rate\) --> \(1=12*\frac{6}{x}\) --> \(x=72\) days needed for 1 machine to complete the job.

To complete the job in 8 days \(\frac{72}{8}=9\) machines are needed.

Difference: 9-6=3.

Answer: B.
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 06 Feb 2012, 06:58
6*12 = 72 units --> 72Units / 8hours = X --> X = 9

Answer B
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 03 May 2012, 09:47
This is how I did it

6 machines in 1hr do 1/12 job
in 1 hr, 1 machine do 1/(12*6) job
In 8 days 1 machine do 8/(12*6)=1/9

Thus there is a need of 9 machine.

But I forgot to minus and get the difference so still get this question wrong.
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 14 Nov 2012, 00:32
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\(Rate of machine = \frac{1}{m}\)

Draw the equation for 6 machines take 12 days:
\(\frac{6}{m}=\frac{1}{12}\)
\(m=72 days\)

Let's look for the number of machines to work for 8 days:
\(\frac{N}{72}=\frac{1}{8}\)
\(N=\frac{72}{8}=9 machines\)

Answer: 9 - 6 machines = 3 machines more

B
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Six machines, each working at the same constant rate, together c [#permalink]

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New post 30 Apr 2013, 23:27
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njss750 wrote:
6 machines each working @ the same constant rate together can complete a certain job in 12 days. How many additional machines are reqd (each working at same constant rate) to finish the job in 8 days?
2
3
4
6
8

Pl xplain with wkgs


6 x 12 = (6+x) x 8

9 = 6+x

x=3
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Re: 6 machines each working @ the same constant rate together [#permalink]

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New post 01 May 2013, 01:06
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You can solve this problem without any equations. Just to calculate the rate of 1 machine.

The rate of 1 machine is \(\frac{1}{6*12}=\frac{1}{72}\) part per day.

So, 1 machine in 8 days can do \(\frac{8}{72}=\frac{1}{9}\).

So, to finish the job in 8 days we need 9 machines. Therefore 3 additional machines are required.

The answer is B.
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 12 Aug 2013, 11:52
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8


Somehow, I found below method to be working for me -
6 Machines in 12 Days do 1 Work i.e. in notation form
6M * 12D = 1W,
so 1M * 1D = [1/(6*12)] W
How many Machines in 8 Days will complete 1 Work? i.e.
xM * 8D = [(x*8)/(6*12)] W = 1W

Solving for x in [(x*8)/(6*12)] = 1, we get x = 9 i.e. 9 Machines in 8 Days will do 1 Work. So 9-6=3 Machines more are required.

Ans - B
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 12 Aug 2013, 12:50
srkaleem wrote:
Six machines, each working at the same constant rate, together can complete a job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

Here, 6 × 1/X = 1/12 or, X=72 . 2nd case, n × 1/72 = 1/8 or, n = 9 . additional = 9-6 = 3
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 25 Jul 2014, 23:04
6 machines - > 12 days to complete the work;

1/12 th of the work is completed by 6 machines in one day.
1/8 th of the work will be completed -- ??? (how many more machines required )

(1/8 *6)/1/12 = 9 ;
therefore 3 additional machines are required.
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 25 Aug 2014, 05:37
since machine and work in inversely related. thus it is inverse proportion

6 x 12 = 8 x N (let n be the number of person required.)

N=9

thus the number of additional person is 9-6 = 3
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 26 Aug 2014, 01:57
6 Machines do \(\frac{1}{12}\) work in 1 day

We require \(\frac{1}{8}\) work to be done in 1 day

Multiplication factor\(= \frac{\frac{1}{8}}{\frac{1}{12}} = \frac{1}{8} * 12 = \frac{3}{2}\)

Additional machines required \(= 6 * \frac{3}{2} - 6 = 9 - 6 = 3\)

Answer = B
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 26 Dec 2014, 15:00
Six Machines:combined rate=6x
Time=12
Let Job be J

6x*12=J

Let M be the number of machines required to complete job in 8 days
Then
Mx*8=J

6x*12=Mx*8

M=9

Additional=9-6=3

Is this approach correct??
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Re: Six machines, each working at the same constant rate [#permalink]

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New post 19 Feb 2016, 10:18
Not sure if this helps or over-complicates but 6 = 3*2 12 = 3*2*2

so if you move one of the 2s over to the 12 side and one of the three over to the 6 side, you would have 9*8. Basically, if one part of the multiplication goes down, the other part must go up in order to equal the same job. Might be overkill in this simple question but could come in handy on a harder one.
Re: Six machines, each working at the same constant rate   [#permalink] 19 Feb 2016, 10:18
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