Shrija Roy 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 work at the same constant rate?

(A) 12

(B) 13

(C) 14

(D) 15

(E) 16

The rate of 12 workers is 60/9 = 20/3.

We can let n = the rate of 27 workers and create the proportion:

12/(20/3) = 27/n

36/20 = 27/n

9/5 = 27/n

9n = 5 x 27

n = 15

So it will take 27 workers 180/15 = 12 minutes to pack all the boxes.

Alternate Solution:

Since twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes, it will take them 9 x 3 = 27 minutes to pack 180 boxes.

Since the number of minutes to pack 180 boxes will decrease as the number of workers increases, we can set up an inverse proportion to determine how much time it will take 27 workers to pack 180 boxes. Let t denote the time, in minutes, required for 27 workers to pack 180 boxes.

(12)(27) = (27)(t)

t = 12

Answer: A

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