Consider the cascade of two tanks shown in, with V1 = 100 (gal) and V2 = 200 (gal) the vol...

Consider the cascade of two tanks shown in, with V1 = 100 (gal) and V2 = 200 (gal) the volumes of brine in the two tanks. Each tank also initially contains 50 lb of salt. The three flow rates indicated in the figure are each 5 gal/min, with pure water flowing into tank 1. (a) Find the amount x(t) of salt in tank 1 at lime t. (b) Suppose that y(t) is the amount of salt in tank 2 at time t. Show first that

and then solve for y{t), using the function x(t) found in part (a), (c) Finally, find the maximum amount of salt ever in tank 2.

FIGURE. A cascade of two tanks.