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