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A new copy machine can run off 1,500 workbooks in 8 hours, while it ta

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A new copy machine can run off 1,500 workbooks in 8 hours, while it ta  [#permalink]

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New post 07 Aug 2019, 03:45
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C
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E

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Question Stats:

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A new copy machine can run off 1,500 workbooks in 8 hours, while it takes on older copy machine 12 hours to do the same job. What is the total number of hours that it would take both copy machines working at the same time, but independently, to run off the 1,500 workbooks?

(A) 4.4
(B) 4.6
(C) 4.8
(D) 5
(E) 10

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Re: A new copy machine can run off 1,500 workbooks in 8 hours, while it ta  [#permalink]

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New post 07 Aug 2019, 04:01
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Work rate of new copier \(= \frac{1500}{8} = \frac{375}{2}\)

Work rate of old copier \(= \frac{1500}{12} = \frac{250}{2}\)

Combined work rate \(= \frac{375}{2}+\frac{250}{2}=\frac{625}{2}\)

So we have

\(\frac{625}{2}*hours=1500\)

Hours\(=\frac{1500*2}{625}=4.8\)

Answer is (C)

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Re: A new copy machine can run off 1,500 workbooks in 8 hours, while it ta  [#permalink]

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New post 07 Aug 2019, 04:16
as all the work done by both machines and the combined rate work is same treat 1500 copies as 1 work

so new m/C 1 work in 8 hrs
so in 1 hr -------------1/8 work

similarly for old M/C
1hr----------------1/12 work

net work by both m/c in 1 hr = 1/8+1/12= 20/96

so time taken will be 96/20 hrs to complete one work therefore 1500 copies
=4.8 hrs
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Re: A new copy machine can run off 1,500 workbooks in 8 hours, while it ta  [#permalink]

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New post 07 Aug 2019, 04:17
Bunuel wrote:
A new copy machine can run off 1,500 workbooks in 8 hours, while it takes on older copy machine 12 hours to do the same job. What is the total number of hours that it would take both copy machines working at the same time, but independently, to run off the 1,500 workbooks?

(A) 4.4
(B) 4.6
(C) 4.8
(D) 5
(E) 10



Time needed for both machine to produce 1500 units is given.

1/8 + 1/12

= 5/24

I hrs work done by both machine.

24/5 = 4.8.

Time needed to complete the entire work.

******* 1500 units must be considered as a single work. units are same for both machine. Therefore we don't need to do anything with units.

C is the correct answer.
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Re: A new copy machine can run off 1,500 workbooks in 8 hours, while it ta  [#permalink]

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New post 12 Aug 2019, 11:53
Bunuel wrote:
A new copy machine can run off 1,500 workbooks in 8 hours, while it takes on older copy machine 12 hours to do the same job. What is the total number of hours that it would take both copy machines working at the same time, but independently, to run off the 1,500 workbooks?

(A) 4.4
(B) 4.6
(C) 4.8
(D) 5
(E) 10



Let T be the number of hours to complete the job when both machines are running. We can create the following equation:

1500/8 * T + 1500/12 * T = 1500

T/8 + T/12 = 1

Let’s multiply each side by 24:

3T + 2T = 24

5T = 24

T = 4.8 hours

Answer: C
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Re: A new copy machine can run off 1,500 workbooks in 8 hours, while it ta   [#permalink] 12 Aug 2019, 11:53
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