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# Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes.

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Math Expert
Joined: 02 Sep 2009
Posts: 45302
Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. [#permalink]

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10 May 2018, 01:29
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Difficulty:

25% (medium)

Question Stats:

86% (01:29) correct 14% (06:29) wrong based on 29 sessions

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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

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Re: Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. [#permalink]

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10 May 2018, 02:09

Solution

Given:
• 12 workers pack boxes at a constant rate of 60 boxes in 9 minutes
• All workers work at the same constant rate

To find:
• How many minutes would 27 workers take to pack 180 boxes

Approach and Working:
• 12 workers pack 60 boxes in 9 minutes
Or, 12 workers pack 1 box in $$\frac{9}{60}$$ minutes
Or, 1 worker packs 1 box in $$\frac{9}{60}$$ * 12 minutes
Or, 27 workers pack 1 box in $$\frac{9}{60} * 12 * \frac{1}{27}$$ minutes
Or, 27 workers pack 180 boxes in $$\frac{9}{60} * 12 * \frac{1}{27}$$ * 180 minutes = 12 minutes

Hence, the correct answer is option A.

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Re: Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. [#permalink]

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10 May 2018, 02:23
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Bunuel 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

Since 12 workers take 9 minutes to pack 60 boxes,
27 workers(which is $$\frac{9}{4}$$ times the workers) take 9 minutes to pack $$\frac{9}{4}*60 = 135$$ boxes.

Now, we know that 27 workers pack 135 boxes in 9 minutes.

In order to pack 180 boxes, they would need $$\frac{180}{135}*9 = \frac{4}{3}*9 = 12$$ minutes.

Therefore, the workers(working at the same constant rate) take 12 minutes(Option A) to pack 180 boxes.
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Re: Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. [#permalink]

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10 May 2018, 03:26
Bunuel 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

Rate of 12 workers = 60/9 boxes / minutes

Rate of 1 worker = (60/9) * (1/12 ) = 5/9 boxes / minutes

Rate of 27 workers = 5/9 * 27 = 15 boxes / minutes

So, to pack 180 boxes time taken = 180/15 = 12 minutes

(A)
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Re: Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes. [#permalink]

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13 May 2018, 17:57
Bunuel 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

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Re: Twelve workers pack boxes at a constant rate of 60 boxes in 9 minutes.   [#permalink] 13 May 2018, 17:57
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