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

One approach is to use the following equation:

(machines)(time) / output = (machines)(time) / output

In the equation above:

Machines and time are INVERSELY PROPORTIONAL.

As the number of machines increases, the amount of time required to produce the same output decreases.

Machines and output are DIRECTLY PROPORTIONAL.

As the number of machines increases, the amount of output also increases.

Time and output are also DIRECTLY PROPORTIONAL.

As the amount of time increases, the amount of output also increases.

In the problem above:

(12 machines)(8 days)/(1 shipment) = (x machines)(6 days)/(1 shipment)

12*8 = 6x

16 = x.

Since the number of machines must increase to 16 from 12, the number of additional machines required = 16-12 = 4.

The correct answer is

C.

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