Consider the cascade of two tanks shown in Fig. 1.5.5, 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 fig- ure are each 5 gal/min, with pure water flowing into tank 1. (a) Find the amount x(t) of salt in tank 1 at time t. (b) Suppose that y(t) is the amount of salt in tank 2 at time t. Show first that dy 100 200 5x 5y dt and then solve for y(t), using the function x(t) found in part (a). Tank 1 Volume V, Amount x Tank 2 Volume V2 Amount y FIGURE 1.5.5. A cascade of two tanks.

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