SOLUTION: When a tank is being drained, the rate of flow varies directly as the square root of the depth of the liquid. In a tank, a liquid 45 inches deep is flowing out at a rate of 4 gal/m

Question 1158655: When a tank is being drained, the rate of flow varies directly as the square root of the depth of the liquid. In a tank, a liquid 45 inches deep is flowing out at a rate of 4 gal/min. How fast is it flowing in gal/min when the level is 20 inches?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let R equal the rate of flow.
let D equal the depth of the liquid.
the formula is R = k * sqrt(D).
when D = 45 inches deep, the water is flowing out at a rate of 4 gallons per minute.
how fast is it flowing when the depth is 20 inches.
firt you want to find k, the constant of variation.
then you want to use that value of k to get your answer.
when D = 45 inches and the water is flowing out at a rate of 4 gallons per minute, the formula becomes:
4 = k * sqrt(45).
solve for k to get:
k = 4 / sqrt(45).
when D = 20 inches and k = 4 / sqrt(45), then the formula becomes:
R = 4 / sqrt(45) * sqrt(20).
this makes R = 2.66666667.

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