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A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes.

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Bunuel
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A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink] New post   04 Feb 2021, 04:45
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A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. The inlet pipe fills water into the tank at the rate of 4 cubic inches/min and the 2 outlet pipes empty it out at the rates of 14 cubic inches/min and6 cubic/min respectively. If all 3 pipes opened when the tank is full, in how much time is it emptied?

(A) 777.6 hrs
(B) 90 hrs.
(C) 80 hrs
(D) 77.76 hrs.
(E) 70 hrs.
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A
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NJ997
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Re: A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink] New post   04 Feb 2021, 11:25
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Volume of tank = 432 cubic feet = \(432 * 12^3\) cubic inches

Since the water comes in at the rate of 4 cubic inches/min and goes out at (14+6) cubic inches/min,
we can say that the water empties out at a net rate of \(20 - 4 = 16\) cubic inches/min

Therefore,
if 16 cubic inches goes out in 1 min, then,
432 cubic inches will empty out in \(\frac{1}{16} * 432 * 12^3\) = 46656 mins = 777.6 hrs

I think the answer is (A)
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Re: A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink] New post   04 Feb 2021, 10:57
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Conversion: \(1 \ foot = 12 \ inches\)

Time taken to empty the tank be \(x\).

\(12^3*432+4x-14x-6x=0\)

\(16x=432*12^3\)

\(x= 27*1728 = 46656 \ min=\frac{46656}{60} \ hr =777.6\)

Ans A
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Re: A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink] New post   18 Feb 2021, 14:30
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Bunuel wrote:
A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. The inlet pipe fills water into the tank at the rate of 4 cubic inches/min and the 2 outlet pipes empty it out at the rates of 14 cubic inches/min and6 cubic/min respectively. If all 3 pipes opened when the tank is full, in how much time is it emptied?

(A) 777.6 hrs
(B) 90 hrs.
(C) 80 hrs
(D) 77.76 hrs.
(E) 70 hrs.

Solution:

We see that the net rate of the pipes is 4 - 14 - 6 = -16 in^3/min. That is, water is pouring out of the tank at a rate of 16 in^3/min. Since 432 ft^3 = (432 x 12^3) in^3, it takes (432 x 12^3) / 16 = (27 x 12^3) minutes or (27 x 12 x 12^2) / 60 = (27 x 12^2) / 5 = 777.6 hours to empty the tank.

Answer: A
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Re: A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink] New post   23 Oct 2023, 23:09
normally in this type of questions official GMAT gives the conversion, if not how an not american can know it :)
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Re: A tank of volume 432 cubic feet has one inlet pipe and2 outlet pipes. [#permalink]
23 Oct 2023, 23:09
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