Question

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7. Two brine tanks are connected as shown below. Tank 1 contains 50 gallons of brine, which initially has 15 Ibs of salt. Tank 2 initially contains 25 gallons pure water. The flow rate r from tank to tank is 10 gallons per minute. Assume that the concentration of brine in each tank is (miraculously) kept uniform by stirring. a. Write a system of differential equations which models the amount of salt in Tank 1 and Tank 2, call them x, and x, , after / minutes. (3 pts) b. Solve your system from part a - meaning, find algebraic expressions for both x, and x, as function of time, f. Describe what happens to the amounts of salt in the two tanks in the long- run (ie. as if the process went on indefinitely) (8 pts) Tank I Tank 2

Answer 1

g

$\frac{i , _{,}}{i t} o ng el 0, i t_{t}, 0, i t_{o}$

$\frac{i , _{i}}{i t} o 0, i t_{t} ng el 0, i t_{o}$

u

$t_{t} x x t o, 0, t x^{ac, 0 x l t}$

$t_{o} x x t o t ng el t x^{ac, 0 x l t}$