The initial values are p(0)=430

q(0)=475

Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 20 L (liters) of water and 430 g of salt, while tank 2 initially contains 90 L of water and 475 g of salt. Water containing 30 g/L of salt is poured into tank1 at a rate of4 L/min while the mixture owing into tank 2 contains a salt concentration of 15 g/L of salt and is flowing at the rate of 2 L/min. The two connecting tubes have a ow rate of 6 L/min from tank 1 to tank 2; and of 2 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 6 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 often too complicated to even write down precisely, much less solve.) How does the water in each tank change over time? Letp(t) and q(t) be the amount of salt in g at time t in tanks 1 and 2 respectively. Write differential equations forp and q. (As usual, use the symbolsp and q rather than p(t) and q(t).)