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An empty swimming pool with a capacity of 5,760 gallons is being fille

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An empty swimming pool with a capacity of 5,760 gallons is being fille  [#permalink]

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New post 26 Sep 2018, 05:14
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:13) correct 46% (02:44) wrong based on 24 sessions

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An empty swimming pool with a capacity of 5,760 gallons is being filled with a pipe at the rate of 12 gallons per minute. An empty pipe that has the capacity to empty (3/4)th of the pool in 9 hours is also in operation. If the pool is already half-filled, and if both the pipes are in operation simultaneously, how many hours would it take to fill the pool to its full capacity?

(A) 6
(B) 12
(C) 24
(D) 36
(E) 72

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Re: An empty swimming pool with a capacity of 5,760 gallons is being fille  [#permalink]

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New post 28 Sep 2018, 07:18
one pipe adds 12 galons per minute allowing it to fill up the pool in 480 minutes (5760 / 12) or 8 hours
the other pipe can drain the pool 3/4 in 9 hours --> drain the full pool in 12 hours
12 hours is 720 minutes meaning the galons per minute draining of this pipe is 8

there's no need to even do the division here since 8h x 12g/min = 12h x 8g/min
the number just change sides
so 1 pipe adds 12g while the other drains 8g meaning there's a net difference of 4g/min

since the pool is half full it's at 5760/2 = 2880g
and still needs 2880g to be filled

at 4g/min this means 720mins or 12hours

B

kudos if the explanation helped
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Re: An empty swimming pool with a capacity of 5,760 gallons is being fille  [#permalink]

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New post 28 Sep 2018, 07:29
Pool capacity = 5,760 gallons

Rate of incoming per hour = 12*60 gallons per hour=720
Rate of outgoing per hour = \((3/4)*(5760)*1/9=5760/12 = 480\)

Effective Rate = 720-480 = 240 per hour

If the pool is already half-filled it needs to fill 5760*1/2= 2880

Time taken to fill 2880 at the rate of 240 gallons per hour = 2880/240 = 12 hours
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Re: An empty swimming pool with a capacity of 5,760 gallons is being fille  [#permalink]

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New post 28 Sep 2018, 07:41
Basically we needed to find time (This approach is not time consuming just the explanation makes it look like one )

Work = Rate * Time

Time = Remaining Work/Combined Rate

Remaining work = 2880 G
Combined Rate = Ra - Rb

Ra - Rate of the inlet pipe
Rb - Rate of the outlet pipe

Converting the rates in minutes will be easy

Rb => 8 G/min
9 hours = 4320 G
1 hour = 480 G
1 min = 480/60 = 8 G/min

Ra => 12 G/min

Now
Time = 2880/(12-8)
Time = 720 mins

Convert this to hours 720/60 = 12 hours

Answer option B
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Re: An empty swimming pool with a capacity of 5,760 gallons is being fille &nbs [#permalink] 28 Sep 2018, 07:41
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