Differential Equations class TwotanksT1andT2contain50gallons

Differential Equations class:

Twotanks,T1andT2,contain50gallonsand100gallonsofsaltsolutions,respectively. A solution with 2 pounds of salt per gallon is pumped into T1 from an external source at a rate of 1 gal/min; a solution with 3 pounds of salt per gallon is pumped into T2 from an external source at a rate of 2 gal/min. The solution from T1 is pumped into T2 at 3 gal/min, and the solution from T2 is pumped into T1 at 4 gal/min. T1 is drained at 2 gal/min and T2 is drained at 1 gal/min. Let Q1(t), Q2(t) be the number of pounds of salt in T1, T2, respectively, at time t > 0. Derive a first order system of differential equations for Q1, Q2. Assume that both mixtures are well stirred.

Solution