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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

**g**

$iti,_{,}aciniaong el0,it_{t},0,it_{o}$

$iti,_{i}aciniao0,it_{t}ng el0,it_{o}$

**u**

$t_{t}xxto,0,tx_{ac,0xlt}$

$t_{o}xxtotng eltx_{ac,0xlt}$

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