Hi All,
We're told that twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. We're asked how many ADDITIONAL machines, each running at the same constant rate, would be needed to REDUCE the time required to complete a shipment BY two days.
In these types of 'work' questions, it often helps to calculate the total amount of work needed, then consider the other variables involved. Here, since we have 12 machines EACH working for 8 days, the total amount of work to complete a shipment would be...
(12 machines)(8 days each) = 96 machine-days of work
Thus, 1 machine would need 96 days to complete the job
2 machines would need 48 days each to complete the job
3 machines would need 32 days each to complete the job
Etc.
We're asked to reduce the total time by 2 days, meaning that the job should take 6 days to complete. That would require...
(96 machine days of work)/(6 total days) = 16 machines needed, each working for 6 days. We already have 12 machines, so we would need 4 more machines.
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