(Solved): Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 90L (itte ...

Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains $90\mathrm{L}$ (itters) of water and $335\mathrm{g}$ of sall, while tank 2 initially contains $40\mathrm{L}$ of water and $465\mathrm{g}$ of salt Water containing $35\mathrm{gh}$ of salt is poured into tank1 at a rate of $1\mathrm{Lmin}$ while the mixture flowing into tank 2 contains a salt concentration of $30\mathrm{g}/\mathrm{L}$ of satt and is fowing at the rate of $3.5\mathrm{L}/\min$. The wo connecting lubes have a now rate of 5 Limin from tank 1 to tank 2 , and of 4 Limin from tank 2 back to tank 1 . Tank 2 is drained at the rate of $45\mathrm{L}/\min$ You may assume that the solutions in each tank are thoroughly mixed so that the concentration of the mixture leaving any tank along any of the tubes has the same concentration of salt as the tank as a whole (This is not completely realistic, but as in real physics, we are going to work with the approximate, rather than exact description. The 'real' equations of physics are offen too complicated to even write down precisely, much less solve.) How does the water in each tank change over time? Let $p(t)$ and $q(t)$ be the arnount of salt in $g$ at time t in tanks 1 and 2 tespectively Wite differenial equations for $p$ and $q$ (As usual, use Ithe symbols $p$ and $q$ rather than $p(t)$ and $q(t))$ $q^{?}=$ Give the initial values $\left[\begin{array}{l}p(0)\\ q(0)\end{array}\right]=[$