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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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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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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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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]

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06 Feb 2012, 05:58
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6*12 = 72 units --> 72Units / 8hours = X --> X = 9

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

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03 May 2012, 08:47
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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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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]

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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]

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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]

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12 Aug 2013, 10:52
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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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12 Aug 2013, 11:50
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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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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]

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25 Aug 2014, 04:37
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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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26 Aug 2014, 00:57
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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]

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26 Dec 2014, 14:00
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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??

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

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19 Feb 2016, 09:18
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.

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

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13 May 2016, 22:53
Can someone please verify my approach to this problem? I solved the problem with unitary method as given below:

6 machine do a job in 12 days

1 machine can do tha same job in 12/6 = 2 days.

Rate of 1 machine = 1/2

now we need the rate to be = 1/8

so, (1/2) ^x = 1/8 => x = 3.

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

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13 May 2016, 23:08
powellmittra wrote:
Can someone please verify my approach to this problem? I solved the problem with unitary method as given below:

6 machine do a job in 12 days

1 machine can do tha same job in 12/6 = 2 days.

Rate of 1 machine = 1/2

now we need the rate to be = 1/8

so, (1/2) ^x = 1/8 => x = 3.

Hi,
you are wrong in highlighted portion..
If 6 machine take 12 days, 1 machine will ofcourse take MORE time so 12*6 = 72 days
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Re: Six machines, each working at the same constant rate [#permalink]

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11 Jul 2016, 15:02
This is an inversely Proportion exercise.
Days=K/Machines (as number of machines goes up, number of days goes down).
12=K/6, so K=72.
Then using the same formula: 8=K/X, 8=72/X, X=9 machines.
You need to add 3 to the initial 6 machines to get the job done in 8 days.

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

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24 Aug 2016, 05:08
6 Machines ------ 12 Days ----- X
1 Machine ----- 12 Days * 6 = 72 Days ----- X

We want to do the job X in 8 days ---> 72 Days / 8 Days = 9 ---> We need 9 machines (i.e. 3 additional machines).

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

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25 Sep 2016, 08:29
I did in the below way.
Let x be the rate of each machine. There are 6 machines working together and so combined rate is 6x per day.
Given currently it is taking 12 days. So, 6x=1/12
Therefore, x=1/72 --> rate of each machine

Let 'a' be the # of machines to be added with the existing 6 machines to complete the task in 8 days.
Thus, the combined rate per day to complete the task in 8 days is,
(1/72) * a +6*(1/72)=1/8
Solving this will give a=3
So (B)

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Re: Six machines, each working at the same constant rate   [#permalink] 25 Sep 2016, 08:29

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