Wo full 100 gallon tanks are connected by two tubes. One tube pumps uid from tank A to tank B at a rate of 3 gallons per minute and the other tube pumps uid from tank B to tank A at the same rate. Initially, tank A contains pure water and tank B contains water with 2 grams of chlorine mixed in. Let QA(t) be the amount of chlorine in tank A at time t and let QB(t) be the amount in tank B at time t. (a) Write down the two ODEs that describe QA(t) and QB(t). (b) Move the common prefactors on the side with no derivatives to the side with time derivative and choose a new time scale τ = αt (constant α) to eliminate the prefactors (this is nondimensionalization again). (c) Solve the general solution of QA(t) and QB(t) by solving QA(τ ) and QB(τ ) rst. (d) Use the initial condition provided in the problem to nd QA(t) and QB(t)