A water tank has a square base with each side of length 4 meters. Water enters through a hose at a constant rate of 20 liters per minute. At the same time a valve in the bottom is opening, so that after t minutes, water leaves at a rate of t liters per minute. If the tank starts out filled to a depth of 2 meters, after how many minutes will the tank be empty

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barackodam barackodam · Answer 1 · 2021-01-26T07:53:47+01:00

Answer:

378.33 minutes

Step-by-step explanation:

From the question, we're told that

Length of the side of the square, l = 4 m

Then the current volume of water = (4 m)³ = 64 m³3 = 64,000 Liters

64,000 + [∫(20 - t) dt from 0 to t] = 0, solving the integral, we have

20t - (t^2)/2 = -64,000, multiplying all by 2 so as to eliminate the fraction

40t - t^2 + 128,000 = 0

t^2 - 40t - 128,000 = 0, on solving the quadratic equation(using general formula), we find that

t = 378.33 minutes