Chapter 6.5, Problem 38E

Mixture In Exercises 35-38, consider a tank that at time $t=0$ contains $v_0$ gallons of a solution of which, by weight, $q_0$ pounds is soluble concentrate. Another solution containing $q_1$, pounds of the concentrate per gallon is running into the tank at the rate of $r_1$, gallons per minute. The solulion in the tank is kept well stirred and is withdrawn at the rate of $r_2$, gallons per minute.

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of concentrate per gallon is admitted to the tank at a rate of 5 gallons per minute, and the well-stirred mixture is withdrawn at a rate of 3 gallons per minute.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