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One hose dispenses water at the rate of one gallon per minut

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One hose dispenses water at the rate of one gallon per minut [#permalink] New post 24 Mar 2020, 08:54
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One hose dispenses water at the rate of one gallon per minute, and a second hose dispenses water at the rate of \(1\frac{1}{2}\) gallons per minute. At the same time, the two hoses begin filling a cylindrical pail whose diameter is 14 inches and whose height is 10 inches. Which of the following most closely approximates the water level, measured in inches up from the pail’s circular base, after \(1\frac{1}{2}\) minutes?
[231 cubic inches = 1 gallon]

(A) 3.5
(B) 4.2
(C) 4.8
(D) 5.6
(E) 6.7
[Reveal] Spoiler: OA
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Re: One hose dispenses water at the rate of one gallon per minut [#permalink] New post 25 Mar 2020, 06:50
Given,
231 cubic inch = 1 gallon
converting the rates into in^3/min
1 gallon/min = 231 in^3/min
1.5 gallon/min = 1.5 * 231in^3/min = 346.5in^3/min
combined rate = 231 + 346.5 = 577.5in^3/min
the volume of the pail = 3.142 * 7^2 * 10 =1539.38in^3
time required to fill the pail is ( using W = R*N*T)
1539.38 = 577.5 * 1 * T,
T = 2.665min
therefore the level of water in 1.5 min ,
1.5 * 10/2.665 = 5.62 in
hence answer is D
Re: One hose dispenses water at the rate of one gallon per minut   [#permalink] 25 Mar 2020, 06:50
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One hose dispenses water at the rate of one gallon per minut

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