Consider two brine tanks connected as shown in the figure. The brine solution is pumped from tank 1 into tank 2 at a rate of 10 L/min, and from tank 2 into tank 1 at a rate of 10 L/min. Suppose there are 50 L of brine in tank 1 and 25 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes have elapsed, and let y the amount of salt, in kilograms, in tank 2 after t minutes have elapsed. Assume that each tank is mixed perfectly. a. If x(0) = 5 kg and y(0) = 4kg, find the amount of salt in each tank after t minutes. x(t) = ? y(t) = ? b. as t -> infinity, how much salt is in each tank? in the long run, tank 1 will have ? kilograms of salt in the long run, tank 2 will have ? kilograms of salt
Consider two brine tanks connected as shown in the figure. The brine solution is pumped from tank 1 into tank 2 at a rate of 10 L/min, and from tank 2 into tank 1 at a rate of 10 L/min. Suppose there are 50 L of brine in tank 1 and 25 L of brine in tank 2. Let x be the amount of salt, in kilograms, in tank 1 after t minutes have elapsed, and let y the amount of salt, in kilograms, in tank 2 after t minutes have elapsed. Assume that each tank is mixed perfectly.
a. If x(0) = 5 kg and y(0) = 4kg, find the amount of salt in each tank after t minutes.
x(t) = ?
y(t) = ?
b. as t -> infinity, how much salt is in each tank?
in the long run, tank 1 will have ? kilograms of salt
in the long run, tank 2 will have ? kilograms of salt
Step by step
Solved in 5 steps with 5 images
