Consider the two tank apparatus shown in the figure. Each tank has capacity $600$ liters and initially contains $100$ liters of fresh water. At time $t = 0$, the well-stirred mixing process begins. Suppose that the concentration of brine flowing into Tank 1 via the top tube is $0.75$ kilograms per liter, and that the flow rates are $r_1 = r_3 = 5$ liters per minute, and $r_2 = r_4 = 15$ liters per minute. (a) Determine the volume of solution in each tank as a function of time, $t$, in minutes. $V_1(t) =$ liters $V_2(t) =$ liters (b) Determine the time interval of interest. (The process stops when a tank is full or empty.) Stopping time is minutes. (c) Let $Q_1(t)$ and $Q_2(t)$ denote the amounts of salt (in kilograms) in the tanks at time $t$ (in minutes). Derive the initial value problem with $Q_1(t)$ and $Q_2(t)$ as dependent variables describing the mixing process. Enter $Q_1(t)$ as Q1(t) and $Q_2(t)$ as Q2(t). $\displaystyle \frac{d}{dt}\left( Q_1(t) \right) =$ kg / min $\displaystyle \frac{d}{dt}\left( Q_2(t) \right) =$ kg / min with $Q_1(0) =$ kg and $Q_2(0) =$ kg.