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 The solution in the tank is kept well stirred and is withdrawn at the rate of r₂ gallons per minute.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 full of a solution containing 25 pounds of concentrate. Starting at time t = 0, distilled water is admitted to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.

(a) Find the amount of concentrate Q in the solution as a function of t.

(b) Find the time at which the amount of concentrate in the tank reaches 15 pounds.

(c) Find the quantity of the concentrate in the solution as
t → ∞.