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# Water has been poured into an empty rectangular tank at the rate of 5

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Math Expert
Joined: 02 Sep 2009
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Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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04 Nov 2017, 09:23
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55% (hard)

Question Stats:

62% (02:07) correct 38% (02:09) wrong based on 111 sessions

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Water has been poured into an empty rectangular tank at the rate of 5 cubic feet per minute for 6 minutes. The length of the tank is 4 feet and the width is 1/2 of the length. How deep is the water in the tank? (1 foot = 12 inches)

(A) 7.5 inches
(B) 3 feet 7.5 inches
(C) 3 feet 9 inches
(D) 7 feet 6 inches
(E) 30 feet

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Re: Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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04 Nov 2017, 10:21
If water is poured into the rectangular tank at the rate of 5 cubic feet per minute for 6 minutes
the volume of the tank would be 30 cubic feet.

Volume of rectangular tank = l*b*h

Length(l) = 4 feet
Width(b) = $$\frac{1}{2}$$*length = $$\frac{1}{2}*4 = 2$$ feet

Let the height of the tank be x

4*2*x = 30 => x = $$\frac{15}{4} = 3.75$$ feet = 3 feet 9 inches(because 1 feet = 12 inches) (Option C)
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Re: Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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04 Nov 2017, 10:23
Bunuel wrote:
Water has been poured into an empty rectangular tank at the rate of 5 cubic feet per minute for 6 minutes. The length of the tank is 4 feet and the width is 1/2 of the length. How deep is the water in the tank?

(A) 7.5 inches
(B) 3 feet 7.5 inches
(C) 3 feet 9 inches
(D) 7 feet 6 inches
(E) 30 feet

the Q is basically asking to work on VOLUME of water..

Volume from the flow of water = 5*6 = 30 cubic feet.
so volume in tank = $$30 = 4*2*d......d=\frac{30}{8}= 3 3/4$$
3/4 of a feet = $$\frac{3}{4}*12=9$$ inches
so 3 feet 9 inches
C
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Re: Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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04 Nov 2017, 12:33
answer is C, assuming that the tank was filled to capacity; otherwise, can't be determined
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Re: Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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04 Nov 2017, 20:40
alexjst wrote:
answer is C, assuming that the tank was filled to capacity; otherwise, can't be determined

Hi..
It has got nothing with volume of tank but volume of water in tank. It need not be assumed that it is completely filled. It may be just half or 1/3- doesn't effect the answer
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Re: Water has been poured into an empty rectangular tank at the rate of 5  [#permalink]

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09 Nov 2017, 10:48
After 1 minute, $$\frac{5}{6}$$ of the work is complete. Remaining work is $$\frac{1}{6}$$
The time required to finish the remaining job is $$\frac{1}{5}$$ th of a minute. i.e 12 seconds

If 5 cubic feet is filled in 60 seconds, 12 seconds can fill 1 cubic feet.

Hence the total height is 31 cubic feet.

Now the base of the tank is 4*2 = 8 feet. We can assume the height to be a multiple of 8.
Since 31 is close to 32, the height is a tiny bit less than 4 feet.

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Re: Water has been poured into an empty rectangular tank at the rate of 5 &nbs [#permalink] 09 Nov 2017, 10:48
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