Working at their individual same constant rate, 24 machines can comple

Solution

Given:

• 24 machines can complete a certain production job in 10 hours, all working together
• All individual machines can work at a same constant rate
• On a certain day, 8 machines did not work due to minor malfunction, for the first 2 hours

To find:

• What is the extra time taken, compared to usual days, to complete the job

Approach and Working:
It is given that all machines can work at a same constant rate

Hence, if we assume that each of the machines can complete 1 unit of job every hour, then

• The total job = 1 * 24 * 10 = 240 units

Now, on that given day, 8 machines did not work for the first 2 hours

• Therefore, in the first 2 hours only 16 machines were working
• The job done by the 16 working machines in the first 2 hours = 1 * 16 * 2 units = 32 units

After 2 hours, all the machines were working, hence the time onwards 2 hours will not change the overall time taken

Now, if all machine works, they can complete 24 units work in 1 hour

• Hence, in 2 hours they would have completed 24 * 2 = 48 units of work

At this rate, to compensate the 32 units of work, the time taken = \(\frac{32}{48}\) hrs = \(\frac{2}{3}\) hrs = 40 minutes

Hence, the correct answer is option C.

Answer: C

Given that 24 machines working together at same constant rate, complete a job in 10 hours.

Hence the job requires a total of 24 * 10 = 240 M/c hrs

Now on a particular day, 8 machines are down for the first 2 hours, hence only 16 machines are operating & they provide 16 * 2 = 32 M/c hrs of work.

Hence the job still requires, 240 - 32 = 208 M/c hrs of work to be done.

Now all 24 machines are working together, to complete the remaining 208 M/c hrs of work.

Hence time taken by the 24 machines to finish the remaining 208 M/c hrs of job = 208/24 = 8.66 hrs.

Hence Total time taken to finish the job (including the 2 hr breakdown of 8 machines) = 2 + 8.66 = 10.66 hrs

Extra time taken = 10.66 - 10 = 0.66 hours = 0.66 * 60 =~ 40 mins

Answer C.

Thanks,
GyM

rate of 1 machine per 1 hour=1/240
in 2 hours 24 machines complete 48/240=3/15 of job
in 2 hours 16 machines complete 32/240=2/15 of job
24 machines can complete missing 1/15 of job in (1/15)/(24/240)=2/3 extra hour
2/3 hour=40 minutes
C

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:

GMAT assassins aren't born, they're made,
Rich

24 Machines do 10% wrk in 1hr
16 machines do (10/24)*16 % wrk in 1 hr
16 machines do (10/24)*16*2 % wrk in first 2 hrs = 13.33%

remaining 100-13.33 = 86.66%
Now all machines work together hence we have to divide 86.66 by 10 i.e (86.66 % work / 10% rate of work) = (time) 8.66 hr

total time = 8.66 + 2 = 10.66 hr

extra = 0.66*60 = 40 min

Better solution-

24 machines 10 hrs works - total work: 240 units

As per question

16 machine 10 hrs work + 8 Machine 8 hrs work + 24 machine y hrs work = 240

160 + 64 + 24Y = 240x

24y = 240 - 224
y =16/24
Y= 2/3 hrs

Y= 2/3* 60

Y= 40 mins

egmat , Can you please explain  how you derived 32/48 ? The compensation part is not clear to me . 

­

egmat , cant I think like this ? 

48 units of work is done  in  2 hours
1 unit of work is done  in 2/48 hours

The remaining (48-32) = 16 units of work (extra) is done in 2/48  * 16 = 2/3 hours extra = 40 mins gmatophobia

­