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 5l/min. At the same time another pipe pumps liquid from tank B to tank A at the same rate. At time t=0, kg of a chemical X is dissolved into tank A, and tank B has kg of the same chemical X dissolved into it.

i). Write down the system of differential equations satisfied by x(t) and y(t), the quantity of the chemical X in tanks A and B respectively.

x(t)=x0-t(y0/40-x0/40)

y(t)=y0-(y0/40+x0/40)

dx/dt=t(-y0/40+x0/40)

dy/dt=t(y0/40-x0/40)

ii). Find the eigenvalues and the eigenvectors of the resulting matrix form.

The matrix is

(-1/40 1/40)

(1/40 -1/40)

The eigenvalues are 0 and -2

so the eigenvector are

(-1)

(1 )

and

(1)

(1)

iii). Show that the amount of the chemical X in either tank approaches as t approaches infinity.

i dont have any idea to do this part, can anyone help me? and tell me what i did wrong in the first and second part pls