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Two hoses (X and Y) are filling a pool. Working alone at their individ

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Two hoses (X and Y) are filling a pool. Working alone at their individ  [#permalink]

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New post 08 Oct 2018, 07:14
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C
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Question Stats:

82% (01:58) correct 18% (02:07) wrong based on 79 sessions

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Two hoses (X and Y) are filling a pool. Working alone at their individual constant rates, Hose X could fill the pool in 6 hours and Hose Y could do it in 4 hours. If the two hoses work together to fill half the pool, and then Hose Y finishes alone, how long will it take to fill the pool?

A. 2 hours, 48 minutes
B. 3 hours
C. 3 hours, 12 minutes
D. 3 hours, 24 minutes
E. 3 hours, 48 minutes

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

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New post 08 Oct 2018, 07:21
Bunuel wrote:
Two hoses (X and Y) are filling a pool. Working alone at their individual constant rates, Hose X could fill the pool in 6 hours and Hose Y could do it in 4 hours. If the two hoses work together to fill half the pool, and then Hose Y finishes alone, how long will it take to fill the pool?

A. 2 hours, 48 minutes
B. 3 hours
C. 3 hours, 12 minutes
D. 3 hours, 24 minutes
E. 3 hours, 48 minutes


Find the combined rate

1/6 + 1/4 = 5/12

The time it takes to fill it entirely is 12/5

Half of the pool required time is 6/5

for y alone it takes 4 hours to fill one pool.

So it takes 2 hours to fill half.

6/5 = 1 hour and 12 minutes

Total 3 hours 12 minutes

Answer choice C

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

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New post 08 Oct 2018, 08:26
X alone 6h = work rate 1/6
Y alone 4h= work rate 1/4
X+Y together= 1/6+1/4= 4/24+6/24=10/24=5/12 --> so 15/2h for Pool (work rate* Time= Unit --> 5/12* X = 1 pool --> X(hours)=12/5=2h 24 min (Note: 12/5=2 2/5 --> 2 12*2/60 --> 2h 24/60 h --> 2h 24 min

Since X+Y only fill half of the pool together they take 1h 12 min for the first half.
Then, Y fills the remaining amount on his own. This takes him 2h (since he needs 4h for the complete pool)

Finally the total time is : XY working together time + Y alone time = 1h 12min + 2h = 3h 12min
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Re: Two hoses (X and Y) are filling a pool. Working alone at their individ  [#permalink]

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New post 08 Oct 2018, 08:39
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Bunuel wrote:
Two hoses (X and Y) are filling a pool. Working alone at their individual constant rates, Hose X could fill the pool in 6 hours and Hose Y could do it in 4 hours. If the two hoses work together to fill half the pool, and then Hose Y finishes alone, how long will it take to fill the pool?

A. 2 hours, 48 minutes
B. 3 hours
C. 3 hours, 12 minutes
D. 3 hours, 24 minutes
E. 3 hours, 48 minutes


Let the capacity of the Pool be 12 units

So, Efficiency of Hose X is 2 units/hour & Efficiency of Hose Y is 3 units/hour

COmbined efficiency of Hose X & Hose Y is 5 Units/Hour

Time taken to fill half the pool is 6/5 = 1 Hour 12 Minutes

Now, 6 Units of work is left and time taken by Y to finish it will be 6/3 = 2 Hours...

Thus, Total time taken to fill the Pool is 3 Hours 12 Minutes, Answer must be (C)
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Re: Two hoses (X and Y) are filling a pool. Working alone at their individ   [#permalink] 08 Oct 2018, 08:39
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