Suppose that a large mixing tank initially holds 400 gallons of water in which 1

Question

Suppose that a large mixing tank initially holds 400 gallons of water in which 100 pounds of salt have been dissolved. One brine solution with concentration 5 lb/gal is pumped into the tank at a rate of 4 gal/min. Another brine solution with concentration 1 lb/gal is also pumped into the tank at a rate of 3 gal/min. At the same time, it is pumped out at rate of 6 gal/min. Determine a differential equation for the amount of slat A(t) in the tank at time t > 0. What is A(0)? Solve the differential equation and find A(10)?

Explanation / Answer

A'=5x4+1x3-1x6 =17

solving A(t)=17t+c A(0)=c=100

so A(t)=17t+100

A(10)=270 lb

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