Consider two tanks A and B, each holding 200 litres of water. A pipe pumps water from tank A to tank B at a rate of 5 litres per minute. At the same time another pipe pumps liquid from tank B to tank A at the same rate. At time t = 0, xo kg of a chemical X is dissolved into tank A, and tank B has Yo kg of the same chemical X dissolved into it. 1. Write down the system of differential equations satisfied by x(t) and y(t), the quantity of the chemical X in tank A and B respectively. 2. Find the eigenvalues and eigenvectors of the resulting matrix from. 1 3. Show that the amount of the chemical X in either tank approaches (xo + yo) as t 2 approaches infinity.

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