Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow for each lake is 200 liters per hour. Lake Alpha contains 500 thousand liters of water, and Lake Beta contains 400 thousand liters of water. A truck with 400 kilograms of KoolAid drink mix crashes into Lake Alpha. Assume that the water is being continually mixed perfectly by the stream. a. Let x be the amount of KooIAid, in kilograms, in Lake Alpha 15 hours after the crash. Find a formula for the rate of change in the amount of KoolAid, (ix/aft, in terms of the amount of KoolAid in the lake 3:. :: : C] kg/hour b. Find a formula for the amount of KooIAid, in kilograms, in Lake Alpha t hours after the crash. $05) = C] kg c. Let y be the amount of KoolAid, in kilograms, in Lake Beta 15 hours after the crash. Find a formula for the rate of change in the amount of KoolAid, dy/dt, in terms of the amounts 33,31. dy E C] kg/hour d. Find a formula for the amount of KooIAid in Lake Beta t hours after the crash. ya) = C] kg