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Machines A, B, and C can either load nails into a bin or unload nails

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Machines A, B, and C can either load nails into a bin or unload nails [#permalink] New post 30 Nov 2009, 06:57
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Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?

(A) 12 minutes
(B) 15 minutes
(C) 18 minutes
(D) 36 minutes
(E) 54 minutes

OPE DISCUSSION OF THIS QUESTION IS HERE: machines-a-b-and-c-can-either-load-nails-into-a-bin-or-86031.html

Last edited by kirankp on 30 Nov 2009, 08:01, edited 1 time in total.
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Re: Machines A, B, and C can either load nails into a bin or unload nails [#permalink] New post 30 Nov 2009, 07:18
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kirankp wrote:
I guess a similar question was posted by Bunel sometime back.. anyhow here it is

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
(A) 12 minutes
(B) 15 minutes
(C) 18 minutes
(D) 36 minutes
(E) 54 minutes


answer C

A and B together = 1/a + 1/b = 1/6

B and C together = 1/b + 1/c = 1/9

We need to know the answer to 1/a - 1/c

From equation 2: 1/b = 1/9 - 1/c
substitute into equation 1

1/a + 1/9 - 1/c = 1/6
1/a - 1/c = 1/18

18 minutes
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Re: Machines A, B, and C can either load nails into a bin or unload nails [#permalink] New post 25 Jun 2015, 07:42
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kirankp wrote:
I guess a similar question was posted by Bunuel sometime back.. anyhow here it is

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
(A) 12 minutes
(B) 15 minutes
(C) 18 minutes
(D) 36 minutes
(E) 54 minutes


Bumping up. Moderator should edit in answer.
\(\frac{1}{6}\) - \(\frac{1}{9}\) = \(\frac{1}{18}\)
D. 18 minutes.

This works because \(\frac{a+b}{ab}\) - \(\frac{b+c}{bc}\) = \(\frac{c-a}{ac}\) and \(\frac{1}{a}\) - \(\frac{1}{c}\) = \(\frac{c-a}{ac}\)
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Re: Machines A, B, and C can either load nails into a bin or unload nails [#permalink] New post 25 Jun 2015, 07:47
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Re: Machines A, B, and C can either load nails into a bin or unload nails [#permalink] New post 25 Jun 2015, 07:49
mejia401 wrote:
kirankp wrote:
I guess a similar question was posted by Bunuel sometime back.. anyhow here it is

Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
(A) 12 minutes
(B) 15 minutes
(C) 18 minutes
(D) 36 minutes
(E) 54 minutes


Bumping up. Moderator should edit in answer.
\(\frac{1}{6}\) - \(\frac{1}{9}\) = \(\frac{1}{18}\)
D. 18 minutes.

This works because \(\frac{a+b}{ab}\) - \(\frac{b+c}{bc}\) = \(\frac{c-a}{ac}\) and \(\frac{1}{a}\) - \(\frac{1}{c}\) = \(\frac{c-a}{ac}\)


Ans is ok as it is it is C which is 18 and D is 36...
Re: Machines A, B, and C can either load nails into a bin or unload nails   [#permalink] 25 Jun 2015, 07:49
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Machines A, B, and C can either load nails into a bin or unload nails

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