4. Consider the closed two-tank system where mixed brine flows from tank 1 into tank 2 and from tank 2 into tank 1 at the flow rate of r gallons per minute (see the following figure). The initial...

a) Derive the system of differential equations and initial conditions representing this system.

b) Solve for x(t) and y(t), assuming r=10, x(0)=10, y(0)=5, V(tank 1)=25, and V(tank 2)=50.

c) Find the limiting amount as t goes to infinity of salt in each tank

Extracted text: 4. Consider the closed two-tank system where mixed brine flows from tank 1 into tank 2 and from tank 2 into tank 1 at the flow rate of r gallons per minute (see the following figure). The initial amounts x(0) = To and y(0)= yo of salt in the two tanks are given, as are their volumes Vi and V2 gallons. t