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

Question

Five machines at a certain factory operate at the same constant rate. If all five machines, operating simultaneously, take 27 hours to fill a certain production order, how many more hours does it take three of these machines, operating simultaneously, to fill the same production order?

A. 45
B. 36
C. 24
D. 18
E. 9

A. 45
B. 36
C. 24
D. 18
E. 9

gchandana · Answer

Official Explanation
 
Since five machines operating simultaneously take 27 hours to fill the production order, a single machine takes five times as long, (27)(5 hours) = 135 hours, to fill the production order. Three machines operating simultaneously perform the task three times as fast as a single machine, and thus take one-third as long as a single machine. Therefore, three machines operating simultaneously take 135/3 = 45 hours to fill the production order, which is 45 − 27 = 18 more hours than five machines operating simultaneously take.

The correct answer is D.

Bunuel · Answer

Five machines at a certain factory operate at the same constant rate. If all five machines, operating simultaneously, take 27 hours to fill a certain production order, how many more hours does it take three of these machines, operating simultaneously, to fill the same production order?

A. 45
B. 36
C. 24
D. 18
E. 9

A. 45
B. 36
C. 24
D. 18
E. 9

5 machines take 27 hours, so the total work is:

5 * 27 = 135 machine-hours

If 3 machines do the same work, time needed is:

135 / 3 = 45 hours

The question asks how many more hours this takes than 27 hours:

45 - 27 = 18

Answer: D.

Alternatively, since all machines work at the same constant rate, 3 machines work at 3/5 of the rate of 5 machines.

Therefore, 3 machines will take 5/3 as much time as 5 machines.

So the time needed is:

27 * 5/3 = 45 hours.

The question asks how many more hours this is than 27 hours:

45 - 27 = 18.

Answer: D.

MartyMurray · Answer

Five machines at a certain factory operate at the same constant rate. If all five machines, operating simultaneously, take 27 hours to fill a certain production order, how many more hours does it take three of these machines, operating simultaneously, to fill the same production order?

A. 45
B. 36
C. 24
D. 18
E. 9

Basic Approach: Find the rate of one machine and use that to find the answer.

Let the rate of one machine be  R .

Rate × Time = Work

5R × 27 = 1  job

5R = \frac{1}{27}

R = \frac{1}{135}

Find the time 3 machines take to do the job:

(3 × \frac{1}{135}) × T = 1

T = \frac{135}{3}

T = 45

Find the difference to answer the question:

45 - 27 = 18

A. 45
B. 36
C. 24
D. 18
E. 9

Correct answer:   D

SameeranKarpe · Answer

For the same production order, the amount of work is constant.
Since all machines work at the same rate:
 Time is inversely proportional to the number of machines. 
Let the time taken by 3 machines be (x) hours.

5*27 = 3*x

x = 45

Therefore, 3 machines take 45 hours.
The question asks how many  more  hours than 27:

45 - 27 = 18

Answer: 18 hours

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

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

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