Problem Solving

Hi All,

We're told that while working at their individual same constant rate, 24 machines can complete a certain production job in 10 hours when they all work together. However, on a certain day, due to minor malfunction, 8 of those machines were not operating for the first 2 hours. We're asked - relative to 'normal' days - what is the EXTRA time taken to complete the production job on that day.

This is an example of a "Work" questions - and it often helps to first determine the total amount of work needed to complete the job. With 24 machines that each work 10 hours at the same rate, the total amount of work needed to complete a job is (24)(10) = 240 machine-hours of work.

Thus, if we had just 1 machine, then it would need to work 240 hours. If we had 2 machines, they would each need to work 120 hours, etc.

We're told that 8 of the machines do NOT work for the first 2 hours, meaning that the remaining 24 - 8 = 16 machines DO work for those first 2 hours....

(16)(2) = 32 machine-hours of work completed. This leaves 240 - 32 = 208 hours of machine work left to complete.

When all 24 machines are working, 24 machine-hours of work are completed each hour....
208/24 = 8 16/24 hours = 8 2/3 hours of time are then needed to complete the job.
Total time = 2 hours + 8 2/3 hours = 10 2/3 hours.... so the extra 2/3 hours = (2/3)(60 minutes) = 40 minutes extra

Final Answer: C

GMAT assassins aren't born, they're made,
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BTGmoderatorLU wrote: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 not 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

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 2/3 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 2/3 additional hours.

Thus, on the day of the malfunction, the machines had to work for 2 + 8 2/3 = 10 2/3 hours, which is 40 minutes longer than normal.

Answer: C