Cascading Tanks3 Fresh water is poured at a rate of 2 gal/min into a tank A, which initial...

Cascading Tanks3 Fresh water is poured at a rate of 2 gal/min into a tank A, which initially contains 100 gal of a salt solution with concentration 0.5 lb/gal. The stirred mixture flows out of tank A at the same rate and into a second tank B that initially contained 100 gal of fresh water. The mixture in tank B is also stirred and flows out at the same rate. (See Fig. 8.)

FIGURE 2.4.8 Tanks for Problem.

(a) Determine an IVP satisfied by the amount of salt in tank A.

(b) Find the amount of salt in tank A at any time.

(c) Find the IVP satisfied by the amount of salt in tank B.

(d) Determine the amount of salt in tank B as a function of time.