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04 Feb 2021, 04:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:56) correct
36%
(03:02)
wrong
based on 164
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History
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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.
(A) 777.6 hrs
(B) 90 hrs.
(C) 80 hrs
(D) 77.76 hrs.
(E) 70 hrs.
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
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
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)
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)
