VAnswer Q₁ = 391121 + 100 22, 2₁(0) = Q 2₂(0) = Qº 22=92 + 30 21-13022, b. QF = 6(991 +92), Q=20(391 +292) 20. a. c. No 1.5 gal/min d. 10 ≤Q/QF ≤ 2009 1 oz/gal Q₁ (t) oz salt 30 gal water Tank 1 3 gal/min 1.5 gal/min 20. Consider two interconnected tanks similar to those in Figure 7.1.6. Initially, Tank 1 contains 60 gal of water and Qoz of salt, and Tank 2 contains 100 gal of water and Q₂ oz of salt. Water containing q₁ oz/gal of salt flows into Tank 1 at a rate of 3 gal/min. The mixture in Tank 1 flows out at a rate of 4 gal/min, of which half flows into Tank 2, while the remainder leaves the system. Water containing 9₂ oz/gal of salt also flows into Tank 2 from the outside at the rate of 1 gal/min. The mixture in Tank 2 leaves it at a rate of 3 gal/min, of which some flows back into Tank 1 at a rate of 1 gal/min, while the rest leaves the system. a. Draw a diagram that depicts the flow process described above. Let Q₁(t) and Q₂(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions for Q₁ and Q₂ that model the flow process. b. Find the equilibrium values QF and Q in terms of the concentrations q₁ and 9₂. c. Is it possible (by adjusting q₁ and ₂) to obtain QF = 60 and Q = 50 as an equilibrium state? d. Describe which equilibrium states are possible for this system for various values of q₁ and 9₂. Q₂(t) oz salt 20 gal water 2.5 gal/min Tank 2 1 gal/min 3 oz/gal