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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]  05 Feb 2012, 22:28
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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
[Reveal] Spoiler: OA
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Re: Help! GMATPrep question [#permalink]  05 Feb 2012, 22:54
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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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Re: Help! GMATPrep question [#permalink]  06 Feb 2012, 01:04
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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.

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Re: Six machines, each working at the same constant rate [#permalink]  06 Feb 2012, 05:58
6*12 = 72 units --> 72Units / 8hours = X --> X = 9

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Re: Six machines, each working at the same constant rate [#permalink]  03 May 2012, 08:47
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]  13 Nov 2012, 23:32
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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]  30 Apr 2013, 22:27
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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]  01 May 2013, 00:06
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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.

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Re: Six machines, each working at the same constant rate [#permalink]  12 Aug 2013, 10:52
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]  12 Aug 2013, 11:50
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]  25 Jul 2014, 22:04
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]  25 Aug 2014, 04:37
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]  26 Aug 2014, 00:57
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 $$= 6 * \frac{3}{2} - 6 = 9 - 6 = 3$$

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Re: Six machines, each working at the same constant rate [#permalink]  26 Dec 2014, 14:00
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

Is this approach correct??
Re: Six machines, each working at the same constant rate   [#permalink] 26 Dec 2014, 14:00
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