Chapter 6.5, Problem 37E

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 The solulion in the tank is kept well stirred and is withdrawn at the rate of $r_2$, gallons per minute.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 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$t=0$, distilled water is admitted to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.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 pounds) 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 amount of concentrate (in pounds) in the solution as $t\to \infty$.