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# Two hoses (A and B) are filling a pool. Working alone at their individ

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 06:14
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:37) correct 31% (01:36) wrong based on 67 sessions

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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If Hose A works alone for one hour and then Hose B joins after that, how long will it take in total for the pool to be filled?

A. 2 hours
B. 2 hours, 12 minutes
C. 2 hours, 48 minutes
D. 3 hours
E. 3 hours, 12 minutes

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Re: Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 07:31
Bunuel wrote:
Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If Hose A works alone for one hour and then Hose B joins after that, how long will it take in total for the pool to be filled?

A. 2 hours
B. 2 hours, 12 minutes
C. 2 hours, 48 minutes
D. 3 hours
E. 3 hours, 12 minutes

Let the capacity of the Pool be 12 units

So, Efficiency of Hose A is 2 units/hour & Efficiency of Hose B is 3 units/hour

Work completed by A in 1 hour is 2 units, so 10 Units of work is left

Combined efficiency of A & B is 5 units/hour.

So, The time taken to fill 10 units is 10/5 = 2 Hours

Thus, the total time taken to fill the Pool will be 1 + 2 = 3 Hours, Answer must be (D)
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Abhishek....

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Re: Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 07:31
Well if hose A’s rate is 1/6

So in 1 hour it will fill 1/6 of the pool.

Remaining work is 6/6 - 1/6 = 5/6

Now the combined rate is 1/4 + 1/6 = 5/12

Since time = work/rate = (5/6)/(5/12) = 2 hours

2 hours is the time needed for the two hoses combined to fill 5/6 of the pool.

Total time = 1 hour + 2 hours = 3 hours.

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Re: Two hoses (A and B) are filling a pool. Working alone at their individ  [#permalink]

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08 Oct 2018, 07:34
A needs 6h for the complete pool, so in 1h A fills 1/6 of the pool
B work rate is 1/4
A+B together have a rate of = 1/6 + 1/4= 10/24= 5/12

Formula = R*T=W . 5/12*X = 1-1/6 units of pool that still needs to be filled up

5/12 * X =5/6 --> X=5/6*12/5 --> X=2 so after A has worked one hour, both together need additional 2 hours. This results in 3hours in total for filling the pool.

Hence, D
Re: Two hoses (A and B) are filling a pool. Working alone at their individ   [#permalink] 08 Oct 2018, 07:34
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