Problems 35 through 37 deal with the closed three-tank sys- tem of Fig. 7.3.5, which is described by the equations in (24). Mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and from tank 3 into tank 1, all at the given flow rate r gallons per minute. The initial amounts x₁ (0) = x₀ (pounds), 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 deter- mine the limiting amount (as t → + ∞) of salt in each tank. Finally, construct a figure showing the graphs of x₁(t), x₂(1), and x₃ (t).

r = 60, x₀ = 55, V₁ = 60, V₂ = 20, V₃ = 30

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T₁ Flow rate: r T₂ FIGURE 7.3.5. The three brine tanks of Example 4. T3