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

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.

6t=4*27
t=18 hours
27-18=9 fewer hours

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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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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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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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

1/(4*27)=1/108=rate of 1 machine
let t=time
t*6*(1/108)=1
t=18
27-18=9

Time taken my 4 machines= 27 hours.

As the efficiencies of the machines are equal, we can take the time taken by one machine and multiply it by the time taken 4 machines we get the total hours taken by all of them.

So we can find the time taken by 1 machine= 27*4=108 hours. That is basically the time effort of 4 machines will be required by the single machine to complete the work.

6 machines will require= 108/6=18 hours.

More time required by 6 machines=27-18=9 hours.
A
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We can use chain formula here-
P1*D1*H1= P2*D2*H2 where, P D H are person, days and hours respectively.
6*x= 4*27 , ignoring the D since no days are given.
solving for x, we get x=18 hours.

But STOP here and re read the Q again. It says how much LESS time, not how much TIME.
Hence less time = 27-18=9 hours
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