Suppose that there is a system of two interconnected taks. The first tank inital

Question

Suppose that there is a system of two interconnected taks. The first tank initally holds 100 gallons of a brine solution consisting of (9/10) pound of salt per gallon. The second tank initally holds 50 gallons of pure water, The rate at which the mixtures are pumper between th tanks are 10 gal/min.

     a) Write the inital value system of first oreder differential equations that the quantities of salt, Qsub1 (t) and Qsub2 (t) should satisfy in both tanks respectively.

     b) solve the linear inital value system

     c) find out the equilibrium cocnentrations of salt in both tanks. That is, find lim as t approaches infinity Qsub1(t) and lim as t approaches infinity Qsub2(t). Does this agree with what you wouldexpect from a physical interpretation perspective?

Explanation / Answer

http://www.math.dartmouth.edu/archive/m8s00/public_html/hw3sup/mixing.pdf

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