Twelve identical machines, running continuously at the same

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.

Final Answer: C

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AAPL wrote:Manhattan Prep

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. 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?

A. 2
B. 3
C. 4
D. 6
E. 9

OA C

It is given that currently, 12 machines complete the work in 8 days and we want the work to be completed within 8 – 2 = 6 days. Since the number of days are reduced by a factor 6/8 = 3/4, we need a greater number of machines, i.e., a total of 12*(4/3) = 16 machines.

Thus, the number of additional machines = 16 – 12 = 4.

The correct answer: C

Hope this helps!

-Jay
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AAPL wrote:Manhattan Prep

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. 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?

A. 2
B. 3
C. 4
D. 6
E. 9

OA C

We are given that 12 machines have a rate of 1/8. We want the shipment to be completed in 6 days, which means that the rate would be 1/6. We need to determine the number of machines necessary to have that rate of 1/6. We can create the following proportion in which n = the new number of machines:

12/(1/8) = n(/1/6)

Multiplying the left side by 8/8 and the right side by 6/6, we get:

96 = 6n

16 = n

Thus, there would need to be 4 additional machines.

Answer: C