Consider the two-tank connection pictured below. The salt water flows at specified rates and the solution is assumed to be “well-stirred”. Each tank has a capacity of 5000 gal. Initially, Tank 1 has 500 gal. of fresh water and Tank 2 has 800 gal. of salt water with 2 lb of salt dissolved in it. Salt water with a concentration of 1/5 lb/gal enters Tank 1 at a rate of 4 gal/min and the mixture leaves at a rate of 7 gal/min at the same time. Salt water with a concentration of 1/4 lb/gal enters Tank 2 at a rate of 10 gal/min and the mixture leaves at a rate of 9 gal/min at the same time. Additionally, the mixture from Tank 1 flows into Tank 2 at a rate of 3 gal/min and the mixture from Tank 2 flows into Tank 1 at a rate of 8 gal/min. Let Q1(t) and Q2(t) denote the amounts of salt in pounds in Tanks 1 and 2 at time t in minutes. Set up the initial value problems for Q1(t) and Q2(t) at time t. (Do not solve.)
Consider the two-tank connection pictured below. The salt water flows at specified rates and the
solution is assumed to be “well-stirred”. Each tank has a capacity of 5000 gal. Initially, Tank 1 has 500 gal. of fresh water and Tank 2 has 800 gal. of salt water with 2 lb of salt dissolved in it. Salt water with a concentration of 1/5 lb/gal enters Tank 1 at a rate of 4 gal/min and the mixture leaves at a rate of 7 gal/min at the same time. Salt water with a concentration of 1/4 lb/gal enters Tank 2 at a rate of 10 gal/min and the mixture leaves at a rate of 9 gal/min at the same time. Additionally, the mixture from Tank 1 flows into Tank 2 at a rate of 3 gal/min and
the mixture from Tank 2 flows into Tank 1 at a rate of 8 gal/min. Let Q1(t) and Q2(t) denote the
amounts of salt in pounds in Tanks 1 and 2 at time t in minutes. Set up the initial value problems
for Q1(t) and Q2(t) at time t. (Do not solve.)
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