In Exercises consider a tank that at time t = 0 contains v₀ gallons of a solution of which, by weight, q₀ pounds is soluble concentrate. Another solution containing q₁ pounds of the concentrate per gallon is running into the tank at the rate of r₁, gallons per minute. The solution in the tank is kept well stirred and is withdrawn at the rate of r₂ gallons per minute.

A 200-gallon tank is half full of distilled water. At time t = 0, a solution containing 0.5 pound of concentrate per gallon enters the tank at the rate of 5 gallons per minute, and the well- stirred mixture is withdrawn at the rate of 3 gallons per minute.

(a) At what time will the tank be full?

(b) At the time the tank is full, how many pounds of concentrate will it contain?

(c) Repeat parts (a) and (b), assuming that the solution entering the tank contains 1 pound of concentrate per gallon.