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Working together at their respective rates, two hoses fill a pool in 2

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Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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New post 08 Aug 2017, 00:22
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

92% (00:51) correct 8% (00:37) wrong based on 61 sessions

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Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
[Reveal] Spoiler: OA

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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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New post 08 Aug 2017, 00:35
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours


Let the hoses be \(A\) and \(B\).

Given \(A\) and \(B\) hoses together can fill a pool in \(2\) hours.

Therefore \(1\) hour work of \(A\) and \(B\) together is equal to.

\(\frac{1}{A} + \frac{1}{B} = \frac{1}{2}\)

Given \(A\) could fill the pool in \(3\) hours alone.

Therefore, \(A = 3\) hours

\(\frac{1}{3} + \frac{1}{B} = \frac{1}{2}\)

\(\frac{1}{B} = \frac{1}{2} - \frac{1}{3} = \frac{3-2}{6} = \frac{1}{6}\)

\(B = 6\) hours

Therefore \(B\) can fill the pool alone in \(6\) hours.

Answer (E)...

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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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New post 08 Aug 2017, 00:37
Bunuel wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours


Pool is 6 units
Hose A + Hose B = 3 units/hr
Hose A = 2 units/hr

Hose B = 1 unit/hr
Time = 6/1 = 6 hrs
E
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Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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New post 04 Dec 2017, 13:40
Hi All,

This question is a standard example of a Work Formula question (with 2 'entities' working on a job together). When this type of question has no 'quirks' to it (such as 3 or more entities or one of the entities stops working partway through the job), you can use the Work Formula to answer it:

Work = (A)(B)/(A+B) = amount of time to complete the job while working together (where A and B are the two individual times it takes to do the job).

In this prompt, we know that one of the hoses takes 3 hours to do the job alone and that the two hoses (working together) can complete the job in 2 hours....

(3)(B)/(3+B) = 2 hours
3B = (2)(3+B)
3B = 6 + 2B
B = 6 hours

Thus, it would take the second hose 6 hours to fill the pool by itself.

Final Answer:
[Reveal] Spoiler:
E


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Kudos [?]: 3683 [0], given: 173

Re: Working together at their respective rates, two hoses fill a pool in 2   [#permalink] 04 Dec 2017, 13:40
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