Consider two brine tanks connected as shown in the figure. The brine solution is pumped from tank 1 into tank 2 at a rate of $10 \ \mathrm{L/min}$, and from tank 2 into tank 1 at a rate of $10 \ \mathrm{L/min}$. Suppose there are $50 \ \mathrm{L}$ of brine in tank 1 and $25 \ \mathrm{L}$ of brine in tank 2. Let $x$ be the amount of salt, in kilograms, in tank 1 after $t$ minutes have elapsed, and let $y$ the amount of salt, in kilograms, in tank 2 after $t$ minutes have elapsed. Assume that each tank is mixed perfectly.

1. If $x(0) = 9 \ \mathrm{kg}$ and $y(0) = 6 \ \mathrm{kg}$, find the amount of salt in each tank after $t$ minutes.
   $x(t) =$ kilograms
   $y(t) =$ kilograms
   
   
2. As $t \to \infty$, how much salt is in each tank?
   In the long run, tank 1 will have kilograms of salt.
   In the long run, tank 2 will have kilograms of salt.
   (Reread the question and think about why this answer makes sense.)

You can earn partial credit on this problem.