Originally Posted by

**drewms64** So im having some problems figuring out where to start on these 2 related rates problems.

1. For a 5000 gallon tank of water which will drain completely in 40 minutes, the volume of water remaining in the tank after t minutes is given by

V = 5000(1 - (t/40))^2

Find the rate at which water is draining from the tank after 10 minutes.

EDIT: I found an example which showed me that I should make the 5000(1-(t/40))^2 into

V(t)= 5000-250t+((25t^2)/8)

V'(t)= -250+(50/8)(t)

= -250+(50/8)(10min)

= -187.5 gal/min ?

2. Oil spills out of a tanker at a rate of 90 gallons per minute. The oil spreads in a circle with a thickness of 1/8 inch. Given that 1 gallon = 7.5 cubic feet, determine the rate at which the radius of the spill is increasing when the radius reaches 100 feet. V=(depth)(area)

edit: converted the 1/8th inch to ft, V=(.0104ft)(7.5*90) = 7.02ft^3/m , so would that be dV/dt? Not sure where I would go from here