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Bunuel
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Bunuel
The length, width, and depth of a rectangular tank are 6 feet, 5 feet, and 7 feet, respectively. A hose supplies water at a rate of 6 cubic feet per minute. How much time in minutes would it take to fill a conical tank whose volume is three times the volume of the rectangle tank?

A. 90
B. 95
C. 100
D. 105
E. 110

cone vol ; 6*5*7 * 3
and rate ; 6 ft^3 per min
so time ; 5*7*3*6/6 ; 105
IMO D
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Quote:
The length, width, and depth of a rectangular tank are 6 feet, 5 feet, and 7 feet, respectively. A hose supplies water at a rate of 6 cubic feet per minute. How much time in minutes would it take to fill a conical tank whose volume is three times the volume of the rectangle tank?

We have a rectangular tank with the following parameters:
L = 6ft
W = 5ft
D = 7ft

Water fills the tank with the rate = 6ft^3/min
Conical tank Volume = 3 x Rectangular Tank Volume

We need to find out how much time would it require to fill in the Conical Tank.

First of all, let us find the volume of rectangular tank: V = L * D* W = 6 * 7 * 5 = 210 ft^3
Second, the form of the tank does not play any role since we know that the volume of conical tank is three times larger than the volume of rectangular tank. Thus, to find out the time for the tank to fill:
Time = Volume of Conical Tank / Rate = 3 * Volume of Rectangular Tank / Rate
Time = 3 * 210 / 6 = 105 ft^3

Answer: D
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