I have the formula, but can\'t figure out how long it takes to run out, I need t

Question

I have the formula, but can't figure out how long it takes to run out, I need the answer PLEASE !!, how much time it takes to empty? A bathtub is filled with water to a depth of 9 inches, At time t=0, the plug is pulled out and the water begins to run out of the tub. The depth,h(t) in inches, is decreasing at a rate given by ( d h(t))/dt = - (1/pi) sqr root h(t) (with t in seconds). use separation of variables to get a formula for the solution of this differential equation. How long does it take for all but a drop or two of the water to run out of tub?

Explanation / Answer

dh/dt = -(1/pi) sqrt(h) =>dh/sqrt(h) = (-1/pi) dt now integrate the terms on both sides 2 * sqrt(h) = (-1/pi) t + c at t =0 , h=9 => c = 2*3 = 6 therefore eq is 2 * sqrt(h) = (-1/pi) t + 6

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