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# A certain pipe carries water between two tanks such that the height of

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A certain pipe carries water between two tanks such that the height of [#permalink]

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04 May 2017, 05:07
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55% (hard)

Question Stats:

63% (01:31) correct 37% (01:42) wrong based on 140 sessions

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A certain pipe carries water between two tanks such that the height of the water in the first tank is decreasing at a rate of 3 inches per second. If the area of the base of the first tank is 3 times as large the area of the base of the second tank, the tank to which water is flowing, at what rate is the height of the water in the second tank increasing?

A. 27 inches per second
B. 9 inches per second
C. 3 inches per second
D. 1 inch per second
E. 1/3 of an inch per second

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Re: A certain pipe carries water between two tanks such that the height of [#permalink]

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04 May 2017, 05:48
1
Tank from which water is being carried is Tank A
Tank to which the water is being carried to is Tank B

Given infomation : Tank A(area of base) is 3 times (area of base) of Tank B,
Water is flowing from Tank A to Tank B

Since the height of the water in Tank A is decreasing at a rate of 3 inches per second,
and Tank A has 3 times the area, the height of increase in Tank B will be 3 times the height decrease in Tank A
Hence, Tank B will increase at a rate of 9 inches/second(Option B)
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Re: A certain pipe carries water between two tanks such that the height of [#permalink]

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06 May 2017, 17:58
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Bunuel wrote:
A certain pipe carries water between two tanks such that the height of the water in the first tank is decreasing at a rate of 3 inches per second. If the area of the base of the first tank is 3 times as large the area of the base of the second tank, the tank to which water is flowing, at what rate is the height of the water in the second tank increasing?

A. 27 inches per second
B. 9 inches per second
C. 3 inches per second
D. 1 inch per second
E. 1/3 of an inch per second

We are given that the height of the water is decreasing at a rate of 3 inches per second. The water is flowing into another tank that has a base area that is 3 times smaller than that of the first tank. Since the base area of the tank into which the water is flowing is 3 times smaller than the base of the other tank, the rate of the increase in water height will be 3 times the rate that the water height decreases in the other tank. Thus, if the water height is decreasing 3 inches per second in the first tank, it will increase 3 x 3 = 9 inches per second in the second tank.

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Re: A certain pipe carries water between two tanks such that the height of [#permalink]

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07 May 2017, 05:32
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Bunuel wrote:
A certain pipe carries water between two tanks such that the height of the water in the first tank is decreasing at a rate of 3 inches per second. If the area of the base of the first tank is 3 times as large the area of the base of the second tank, the tank to which water is flowing, at what rate is the height of the water in the second tank increasing?

A. 27 inches per second
B. 9 inches per second
C. 3 inches per second
D. 1 inch per second
E. 1/3 of an inch per second

Volume = Base Area * Height of vassel

Base Area of First Tank = 3* Base area of Second Tank
Understand that bigger the base will lead to lesser reduction in height in comparison to other vessel which has smaller base
i.e. Rate of decrease in height*3 = rate of Increase in height (Change in height is inversely proportional to Base areas)

3*3 = rate of Increase in height = 9

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A certain pipe carries water between two tanks such that the height of [#permalink]

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07 May 2017, 06:52
Try "smart" numbers. The logic of above answers is the same, but it was easier for me to see, might be for others.

If a problem doesn't forbid emptying contents of one container into another when different dimensions are at issue but NOT different units, almost always, it helps to assume that one empties into the other. (I started trying to account for -3 inches per second. Bad idea.)

So the volume of water in the first tank, with height of 3 is EMPTIED in 3 seconds.

1. Numbers chosen

Let base area of Tank 1 = 3
Let height of Tank 1 = 3

Base area of Tank 1 is three times that of Tank 2=>

Tank 2 base area= 3/1 = 1

BASE AREA of both is (π*$$r^2$$) - No need to calculate it in volume formula; its value is assigned

2. Volume of water in Tank 1

--> V =(π*$$r^2$$)*h

Base area = 3

Height of water is 3

V=3*3

Volume of water equals 9

3. Find height of Tank 2, into which the water goes. Volume is 9. Same formula, but solve for height (to which water will rise)

9 = (π*$$r^2$$)*h

Base area = 1,so height of water:
9=(1)(h), h=9

Answer B: 9 inches per second
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Re: A certain pipe carries water between two tanks such that the height of [#permalink]

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07 May 2017, 18:36
Bunuel wrote:
A certain pipe carries water between two tanks such that the height of the water in the first tank is decreasing at a rate of 3 inches per second. If the area of the base of the first tank is 3 times as large the area of the base of the second tank, the tank to which water is flowing, at what rate is the height of the water in the second tank increasing?

A. 27 inches per second
B. 9 inches per second
C. 3 inches per second
D. 1 inch per second
E. 1/3 of an inch per second

Let us say that the area of the base of the first tank is 6 square inches. Now 6 x 3 = 18 cubic inches of water is flowing in the other tank. The area of the second tank is 2 square inches. If the volume is 18 cubic inches and area is 2 square inches then the height is 18/2 = 9 inches.

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Re: A certain pipe carries water between two tanks such that the height of [#permalink]

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30 Jun 2018, 02:42
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Re: A certain pipe carries water between two tanks such that the height of   [#permalink] 30 Jun 2018, 02:42
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