Working at their individual same constant rate, 24 machines can complete a certain production job in 10 hours when they

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Working at their individual same constant rate, 24 machines can complete a certain production job in 10 hours when they all work together. On a certain day, due to minor malfunction, 8 of those machines were no operating for the first 2 hours. Compared to normal days, what is the extra time taken to complete the production job on that day?

A. 20 minutes
B. 30 minutes
C. 40 minutes
D. 1 hour
E. 1 hour 20 minutes

The OA is C

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24 machines can complete a production job in 10 hours.
Given that all machines can work at the same constant rate, assuming each machine can complete 1 unit of the job per hour. Then, total job = 24 * 10 = 240 units
On a certain day, 8 machines did not work for the first 2 hours, so, only (24 - 8 = 16) machines were working.
Job done by 16 machines in 2 hours = 16 * 2 = 32 units
If all machines were working, the work done in 2 hours by 24 machines = 24 * 2 = 48 units
$$Extra\ time\ taken\ to\ complete\ the\ job=\frac{32}{40}-\frac{16}{24}=\frac{8}{12}$$
$$=\frac{4}{6}=\frac{2}{3}hours$$
If 1 hour = 60 minutes
$$Then,\frac{2}{3}hours=60\cdot\frac{2}{3}=\frac{120}{3}=40\ minutes$$

Answer = option C

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BTGmoderatorLU wrote:
Tue Mar 16, 2021 5:46 pm
Source: E-GMAT

Working at their individual same constant rate, 24 machines can complete a certain production job in 10 hours when they all work together. On a certain day, due to minor malfunction, 8 of those machines were no operating for the first 2 hours. Compared to normal days, what is the extra time taken to complete the production job on that day?

A. 20 minutes
B. 30 minutes
C. 40 minutes
D. 1 hour
E. 1 hour 20 minutes

The OA is C
Solution:

The rate of 24 machines is 1/10.

On a certain day 16 machines first ran for 2 hours.

The rate of the 16 machines is:

16/n = 24/(1/10)

16/n = 240

16 = 240n

n = 16/240 = 1/15

Thus, when 16 machines work for 2 hours, the fraction of the job completed is 1/15 x 2 = 2/15.

Thus, 13/15 of the job needs to be completed by 24 machines. The time it will take to complete the job is:

(13/15)/(1/10) = 130/15 = 26/3 hours

Therefore, the total time spent on the job is 2 + 26/3 = 32/3 hours = 10 ⅔ hours = 10 hours 40 minutes, which is 40 minutes more than on a normal day.

Alternate Solution:

Since the 24 machines normally require 10 hours to get the job done, the total time required is 240 machine hours.

On the day of the malfunction, only 16 machines were working for the first 2 hours; thus, they accomplished 16 x 2 = 32 machine hours of production.

When all 24 machines were back in production, we see that there were 24 machines that needed to accomplish the remaining (240 - 32) = 208 machine hours of production. This results in 208/24 = 8 ⅔ additional hours.

Thus, on the day of the malfunction, the machines had to work for 2 + 8 ⅔ = 10 ⅔ hours, which is 40 minutes longer than normal.

Answer: C


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