Consider the following system of tanks. Each tank initially contains V1 = 200 gallons and V2 = 300 gallons of fresh water. At time t = 0 minutes, all three valves open up, allowing for a salt brine solution (at a concentration of 2 lbs/gal) to enter the first tank through the first valve. At the same time, the solution is allowed to pass from the first tank into the second tank, and finally, the solution is allowed to exit the second tank, all at the same rate of r = 5 gal/min. (a) Set up a system of differential equations that will allow you to solve for q1(t) and q2(t), which represent the amount of salt (in pounds) in tank 1 and tank 2, respectively, at time t. (b) Solve your system to find q1(t) and q2(t), and then graph them
Consider the following system of tanks. Each tank initially contains V1 = 200 gallons and V2 = 300 gallons of fresh water. At time t = 0 minutes, all three valves open up, allowing for a salt brine solution (at a concentration of 2 lbs/gal) to enter the first tank through the first valve. At the same time, the solution is allowed to pass from the first tank into the second tank, and finally, the solution is allowed to exit the second tank, all at the same rate of r = 5 gal/min.
(a) Set up a system of differential equations that will allow you to solve for q1(t) and q2(t), which represent the amount of salt (in pounds) in tank 1 and tank 2, respectively, at time t.
(b) Solve your system to find q1(t) and q2(t), and then graph them
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