SHOW ALL YOUR WORK AND EXPLAIN STEPS:

Consider a situation where a sugar-water solution solution containing 0.2 lb of sugar per gallon enters tank A at a rate of 3 gallons per minute.

The contents of tank A are kept well mixed and are drained into a second tank, tank B at a rate of 3 gallons per minute.

The contents of tank B are also well mixed and drained into the sewer at a rate of 3 gallons per minute.

Suppose that tank A initially contains 100 gallons of pure water and tank B initially contains 50 gallons of pure water.

Let x = x(t) be the amount of sugar in tank A after t minutes have passed

Let y = y(t) be the amount of sugar in tank B after t minutes have passed.

(a) Set up an initial value problem which can be used to solve for x = x(t).

(b) Set up an initial value problem which can be used to solve for y = y(t).

Note that the differential equation in this part will have both x and y in it.

Note: You do not need to solve the initial value problems from parts (a) and (b).