Differential Equations word problem two

Question

A tank contains 200 liters of fluid in which 30 grams ofsalt is dissolved. Brine containing 1 gram of salt per literis then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

Answer 1

Question: A tank contains 200 liters of fluid in which 30 grams ofsalt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

 

Initial amount of salt in tank is S = 30 gm.

Concentration of brine is Bc = 1 gm/liter

Pump rate is P = 4 liters/min

Salt addition rate = Sr = P*Bc = 4*1 = 4 gm/min 

The number of grams of salt in the tank at time t is: A(t) = S + Sr*t = 30 + 4t gms