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Twelve workers pack boxes at a constant rate of 60 boxes

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Twelve workers pack boxes at a constant rate of 60 boxes [#permalink] New post 13 Mar 2018, 19:41
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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
[Reveal] Spoiler: OA

Last edited by Carcass on 14 Mar 2018, 15:30, edited 1 time in total.
Edited by Carcass
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Re: Work/Rate question [#permalink] New post 14 Mar 2018, 01:15
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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


Given 12 workers pack 60 boxes in 9 min. So 1 worker can pack \(\frac{60}{12}=5\) boxes per 9 minutes or \(\frac{5}{9}\) boxes per minute.

27 workers will pack \(\frac{5}{9} \times 27 =15\) boxes per minute.

Time needed to pack 180 boxes at 15 boxes per minute rate = \(\frac{180}{15}=12\).

SO A is correct!.
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Re: Twelve workers pack boxes at a constant rate of 60 boxes [#permalink] New post 22 Mar 2018, 03:05
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use ratio, such as if 12 workers' rate is 60/9 then 1/12=x/60/9
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Re: Twelve workers pack boxes at a constant rate of 60 boxes [#permalink] New post 13 May 2018, 16:44
Expert's post
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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Re: Twelve workers pack boxes at a constant rate of 60 boxes   [#permalink] 13 May 2018, 16:44
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