6. (5pts) Suppose that we have two tanks, Tank 1 and Tank 2. Tank 1 initially contains 52 liters of a solution and Tank 2 contains 48 liters. In tank 1, we have initially dissolved 5 grams of a certain chemical and in Tank 2 we have initially dissolved 12 grams of the same chemical. Let t denote time, measured in minutes. Let Vi(t) denote the volume of solution in Tank 1 at time t, measured in liters, and let V2(t) denote the volume of solution in Tank 2 at time t, also measured in liters. Let A1(t) denote the amount of chemical in Tank 1 at time t, measured in grams, and let A2(t) denote the amount of chemical in Tank 2 at time t, also measured in grams. A solution containing co grams/liter of the same chemical flows into Tank 1 at a constant rate of r1 liters/minute. The solution in Tank 1 then empties into Tank 2, flowing into Tank 2 at a constant rate of r2 liters per minute. Finally, the mixture flows out of Tank 2 at a constant rate of 73 liters per minute. Assume that the mixtures inside both tanks is kept uniform by stirring. At any time t, the concentration of chemical in Tank 1 is given by ci(t) = Allt and the concentration of chemical in Tank 2 is given by c2(t) = A2 (t) V2 ( t ) (a) Write differential equations describing the rate of change of the volume of solution in the Tank 1 and the volume of solution in Tank 2. What are the initial conditions given? (b) Write differential equations describing the rate of change of amount of chem- ical in Tank 1 and the amount of chemical in Tank 2. What are the initial conditions given