## Question

###### Deal with the closed three-tank system of Fig. 5.2.5, which is described by the equations in (24, Mixed brine flows from tank 1 into tank 2, from tank 2 int $operatorname{tank} 3$, and from tank 3 into tank 1, all at the given flow rate gallons per minute. The initial amounts $x_{1}(0)=x_{0}$ (pounds, $x_{2}(0)=0$, and $x_{3}(0)=0$ of salt in the three tanks are giver as are their volumes $V_{1}, V_{2}$, and $V_{3}($ in gallons $) .$ First solve for the amounts of salt in the three tanks at time

Deal with the closed three-tank system of Fig. 5.2.5, which is described by the equations in (24, Mixed brine flows from tank 1 into tank 2, from tank 2 int $operatorname{tank} 3$, and from tank 3 into tank 1, all at the given flow rate gallons per minute. The initial amounts $x_{1}(0)=x_{0}$ (pounds, $x_{2}(0)=0$, and $x_{3}(0)=0$ of salt in the three tanks are giver as are their volumes $V_{1}, V_{2}$, and $V_{3}($ in gallons $) .$ First solve for the amounts of salt in the three tanks at time $t$, then determine the limiting amount (as $t ightarrow+infty)$ of salt in each tank Finally, construct a figure showing the graphs of $x_{1}(t), x_{2}(t)$ and $x_{3}(t)$. $$ r=10, x_{0}=18, V_{1}=20, V_{2}=50, V_{3}=20 $$

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