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 200 thousand liters of water, and Lake Beta contains 400 thousand liters of water. A truck with 400 kilograms of Kool-Aid drink mix crashes into Lake Alpha. Assume that the water is being continually mixed perfectly by the stream and that the kool-aid is not flowing into Lake Alpha, it has already been mixed in instantaneously. a. Let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. Find a formula for the incremental change in the amount of Kool-Aid, Δx, in terms of the amount of Kool-Aid in the lake x and the incremental change in time Δt.
b. Find a formula for the amount of Kool-Aid, in kilograms, in Lake Alphat hours after the crash.
c. Let y be the amount of Kool Aid in kilograms ın Lake Beta t hours after the crash. Find a formula for the incremental change in the amount of Kool Aid A n terms of the amounts x, y, and the incremental change in time At.
d. Find a formula for the amount of Kool-Aid in Lake Beta t hours after the crash.