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Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
A: 9
B: 12
C: 16
D: 18
E: 24
A: 9
B: 12
C: 16
D: 18
E: 24
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.
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.
18 Jun 2016, 00:37
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tanad
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
A: 9
B: 12
C: 16
D: 18
E: 24
A: 9
B: 12
C: 16
D: 18
E: 24
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)
