Suppose that in the cascade shown in, tank 1 initially contains 100 gal of pure ethanol and tank 2 initially contains 100 gal of pure water. Pure water flows into tank 1 at 10 gal/min, and the other two flow rates are also 10 gal/min. (a) Find the amounts x(t) and y(t) of ethanol in the two tanks at time t ≥ (0). (b) Find the maximum amount of ethanol ever in tank 2.
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