The volume of two tanks are V1 =100 gallons and V2 = 200 gallons .The inflow and outflow rates of the system are r = 10 gallons per minute. Suppose that the two tanks both contain fresh water initially, but the inflow to tank 1 is brine at 2 pounds per minute, so that 2 pounds of salt flow into tank 1 each minute. Write a matrix system of equations for the amounts and of salt in the two tanks after t minutes. Solve the system using matrix methods. Calculate how long it takes for tank 2 to have a salt concentration of 1 pound per gallon.
Please remember to calculate the eigenvalue using det |A-lambda*I|
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The amount of salt in the first tank is x1, thus the concentration is ...
The 5 pages solution describes in full details how to:
1. Convert the problem's text to differential equations.
2. Solve a system of two non-homogeneous first order differential equations using matrices.