sandy wrote:

Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. How many minutes would it take 27 workers to pack 180 boxes, if all workers pack boxes at the same constant rate?

(A) 12

(B) 13

(C) 14

(D) 15

(E) 16

Use the following equation:

\(\frac{workers * time}{output} = \frac{workers*time}{output}\)

In the equation above:

Workers and time are INVERSELY PROPORTIONAL.

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

Workers and output are DIRECTLY PROPORTIONAL.

As the number of workers 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:

Since 12 workers take 9 minutes to pack 60 boxes, and we want to know the time required for 27 workers to pack 180 boxes, we get:

\(\frac{12*9}{60} = \frac{27t}{180}\)

\(\frac{9}{5} = \frac{3t}{20}\)

\(15t = 180\)

\(t = 12\)

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