Consider the cascade of two 300L tanks shown in the figure below. Suppose that tank 1 INITIALLY CONTAINS 300Litres of pure ethanol and tank 2 initially contains 100 litres of pure water. Pure water flows in to tank 1 at a rate of 10 L/Min, the mixture then flows out of t tank 1 and into tank 2 at a rate of 10 L/min. Finally, the new mixture flows out of tank 2 at a rate of 5L/min.
a) find the amounts x(t) and y(t) of ethanol in the two tanks at time t _> 0.
b) how much ethanol whill be in tank 2 when it finally, fills up.
X( t) = amount of ethanol in tank 1 at time ty(t) = amount of ethanol in tank 2 at time t