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

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Math Expert
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124212 [0], given: 12075

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

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08 Aug 2017, 01:22
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:03) correct 19% (01:15) wrong based on 38 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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Kudos [?]: 124212 [0], given: 12075

Director
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 263 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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08 Aug 2017, 01:35
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.

Kudos [?]: 263 [0], given: 261

Director
Joined: 18 Aug 2016
Posts: 502

Kudos [?]: 126 [0], given: 120

GMAT 1: 630 Q47 V29
Re: Working together at their respective rates, two hoses fill a pool in 2 [#permalink]

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08 Aug 2017, 01:37
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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Kudos [?]: 126 [0], given: 120

Re: Working together at their respective rates, two hoses fill a pool in 2   [#permalink] 08 Aug 2017, 01:37
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