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EACHER PRACTICE ANOTHER Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank & contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank 8 are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x, (t) and Xz(t) of salt in tanks A and B, respectively, at time t. pure water mixture 3 gal/min I gal/min mixture mixture 4 gal/min 3 gal/min This system is described by the system of equations dx 1 1 X2 dt 2 x1 + 25 50 dx2 2X1 25 2 X2 dt 25 with Initial conditions x](0) = 25, x2(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, Instead of pure water, a brine solution containing 5 pounds of salt per gallon is pumped Into tank A? dx1 2 dt 25 1+ 50 - +9