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Twelve workers pack boxes at a constant rate of 60 boxes in
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18 Jun 2018, 14:50
18 Jun 2018, 14:50
Expert Reply
00:00
Question Stats:
85% (01:40) correct
14% (02:47) wrong based on 75 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 pack boxes at the same constant rate?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Re: Twelve workers pack boxes at a constant rate of 60 boxes in
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01 Jul 2018, 23:15
01 Jul 2018, 23:15
1
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
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Here,
We know Work = No. of individual * Rate * Time
so 60 = 12 * Rate * 9
or Rate =\(\frac{60}{(12 * 9)}\) = \(\frac{5}{9}\)
Now for 180 boxes ;
Work = No. of individual * Rate * Time
\(180 = \frac{5}{9} * 27 * Time\)
or Time = \(\frac{(180 * 9)}{(5 * 27)}\) = 12
Re: Twelve workers pack boxes at a constant rate of 60 boxes in
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07 Jul 2018, 04:55
07 Jul 2018, 04:55
Expert Reply
Explanation
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Use the first sentence to solve for an individual worker’s rate. Plug in the fact that 12 workers pack boxes at a constant rate of 60 boxes in 9 minutes:
Work = Individual Rate × Number of Workers × Time
60 boxes = (R)(12)(9 minutes)
\(R =\frac{5}{9}\) boxes per minute.
In other words, each worker can pack \(\frac{5}{9}\) of a box per minute. Plug that rate back into the formula, but use the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(180 = \frac{5}{9} \times 27 \times T\)
\(180=15T\)
\(T=12\).
To solve a Rates & Work problem with multiple workers, modify the standard formula Work = Rate × Time to this:
Work = Individual Rate × Number of Workers × Time
Use the first sentence to solve for an individual worker’s rate. Plug in the fact that 12 workers pack boxes at a constant rate of 60 boxes in 9 minutes:
Work = Individual Rate × Number of Workers × Time
60 boxes = (R)(12)(9 minutes)
\(R =\frac{5}{9}\) boxes per minute.
In other words, each worker can pack \(\frac{5}{9}\) of a box per minute. Plug that rate back into the formula, but use the details from the second sentence in the problem:
Work = Individual Rate × Number of Workers × Time
\(180 = \frac{5}{9} \times 27 \times T\)
\(180=15T\)
\(T=12\).
