Problems 31 through 34 deal with the open three-tank system of Fig. 7.3.2. Fresh water flows into

Question:

Problems 31 through 34 deal with the open three-tank system of Fig. 7.3.2. Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₀ (lb), x₂ (0) = 0, and x₃ (0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V₃ (in gallons). First solve for the amounts of salt in the three tanks at time t, then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x₁(1), x₂(t), and x₃(t).

r = 60, x₀ = 40, V₁ = 20, V₂ = 12, V₃ = 60