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Six machines, each working at the same constant rate
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26 Apr 2010, 21:53
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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?
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.
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27 Apr 2010, 06:02
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zz0vlb wrote:
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?
Another solution which is faster is Since each machine works at a constant rate. The time needs to bought down from 12 to 8. So the new time is 2/3 of the original time. Thus to achieve this we need the rate to be 3/2 of original.
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19 Jun 2010, 19:52
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Actually, this was more simple than I thought. When I first saw this, I started to panic thinking it's a rate question. But then I took a step back, and it was the simplest of calculations.
So here's the deal:
12 days -> 6 machines: 8 days -> ?
8 days means you definitely need more machines than the 6 and in such case the equation looks like-
Six machines, each working at the same constant rate, together c
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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
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26 Apr 2010, 22:50
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zz0vlb wrote:
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 each machine work at rate of x days 1/x+1/x+1/x+1/x+1/x+1/x = 1/12 6/x = 1/12 x = 72 now y is number of machines needed to complete job in 8 days so, y/72 = 1/8 y = 9 required = y-x = 3 hence b.
Re: Six machines, each working at the same constant rate
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07 Apr 2018, 10:40
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Hi All,
We're told that 6 machines, working at the same constant rate, can finish a job in 12 days. We're asked for the number of EXTRA machines will you need to finish the job in 8 days?
This type of question is easiest to solve if you convert the info into "work units" Here, we start with 6 machines working for 12 days. This equals (6)(12) = 72 machine-days of work to finish the job.
If we wanted to finish the job in 8 days, it would still take 72 machine-days of work, so we'd need 72/8 = 9 machines.
We already have 6 machines, so we need 3 MORE machines to get the job done in 8 days.
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25 Jun 2018, 12:12
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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
We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.
We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.
Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.
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12 Aug 2013, 12:50
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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?
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12 Aug 2013, 11:52
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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.
I wish I could send you a gratitude note for your awesome time efficient approach mentioned here
Please confirm your two cents: Logic: more the nos of machines -> less no of days
Start with no of machines in initial stage: 6
Now we need to decide to multiply by 12/8 or 8/12 Since we need more no of machines to do the work in less time from 12 to 8 days , we need an improper fraction hence 6 * (12/8) = 9 no of machines.