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Four carpenters can individually complete a particular task

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Four carpenters can individually complete a particular task [#permalink] New post 05 Jun 2012, 09:02
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Question Stats:

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Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9
[Reveal] Spoiler: OA
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Re: Four carpenters can individually complete a particular task [#permalink] New post 05 Jun 2012, 09:21
Expert's post
shradhagrover18 wrote:
Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9


In order three of the carpenters to complete the maximum fraction of the task we should select three fastest carpenters. So, those three who complete the task in 3, 4, and 5 hours.

In 1 hour they will complete \frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}th of the task. So, in \frac{3}{4} hour (45 minutes) they will complete \frac{47}{60}*\frac{3}{4}=\frac{47}{80}th of the job.

Answer: D.

Hope it's clear.
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Re: Four carpenters can individually complete a particular task [#permalink] New post 05 Jun 2012, 14:33
1/3 + 1/4 + 1/5 = 47/60
47/60 * 3/4 = 47 / 80

D
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Re: Four carpenters can individually complete a particular task [#permalink] New post 05 Jun 2012, 17:05
shradhagrover18 wrote:
Four carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if three of the carpenters work together at their respective rates ?

A. 11/15
B. 3/5
C. 11/30
D. 47/80
E. 5/9


Farmer A, B, C, and D

A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour

By intuition we know that the three fastest farmers are A B and C.

As such

(1/3 + 1/4 + 1/5)*(3/4) = ?

47/80 or (D)
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Re: Four carpenters can individually complete a particular task [#permalink] New post 14 Jun 2013, 04:27
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Re: Four carpenters can individually complete a particular task   [#permalink] 14 Jun 2013, 04:27
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