(Solved): Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 60L (iter ...

Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains $$60\mathrm{L}$$ (iters) of water and $$460\mathrm{g}$$ of $$9alt$$ while fank 2 initially contains $$40\mathrm{L}$$ of water and $$185\mathrm{g}$$ of salt. Water containing $$45\mathrm{g}$$ L of salt ia poured into tanki at a rate of $$2.5\mathrm{U}/\min$$ while the moxture flowing into tank 2 contains a salt concentration of $$15\mathrm{gL}$$ of sait and is flowing at the fate of 2 Limin. The fwo connecting fubes have a flow rate of $$6\mathrm{L}$$ min from tank 1 to tank 2 ; and of $$3.5\mathrm{L}$$ miri from tank 2 back to tank 1 . Tank 2 is drained at the rate of $$4.5\mathrm{L}/\min$$. You mny 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 realiatic, but as in mal physics, we are going to work with the approximate, rather than exact description. The 'reaf 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? Lot $$p(t)$$ and $$q(t)$$ be the amount of sat in $$g$$ at time $$t$$ in tanks 1 and 2 respectively. Write differential equations for $$p$$ and $$q$$. As unual, use the symbols $$p$$ and $$q$$ rather than $$p(t)$$ and $$q(t)$$ ) $$p^{?}=$$ $$q^{?}=$$ Give the initial values: $$\left[\begin{array}{l}p(0)\\ q(0)\end{array}\right]=[=[$$