Consider two tanks $T_1$ and $T_2$ with $T_1$ containing $200$ gallons of water in which $50$ pounds of salt is dissolved and $T_2$ containing $100$ gallons of water in which $100lb$ of salt is dissolved. Pure water flows from the outside into $T_1$ at a rate of $4ga\frac{l}{m}in$ and salt solution is circulated at rates of $4ga\frac{l}{m}in$ from $T_1$ to $T_2$ and $2ga\frac{l}{m}in$ from $T_2$ to $T_1.$ If the contents of the two tanks are well$-$mixed and $2ga\frac{l}{m}in$ are also withdrawn from each of the two tanks $T_1$ and $T_2$ to the outside to ensure no liquid volume change in the two tanks or the system, draw the process flowchart and determine the engineering design equations you would need to calculate the salt contents in each tank as a function of time and find the time it would take for the salt contents in the two tanks to be equal. What happens over a long period of time $($i$.$e$.,$ as $t).$ Calculate all values, including eigenvalues and eigenvectors, to $35($i$.$e$.,$ three significant figures!$)$