A large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is pumped out at a rate of 6 gals/min. Find the number A(t) of pounds of salt in the tank at time t. How long (in minutes) will it take for the tank to be empty after this process has started?
A large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is pumped out at a rate of 6 gals/min. Find the number A(t) of pounds of salt in the tank at time t. How long (in minutes) will it take for the tank to be empty after this process has started?
Tank has been filled to capacity with 300 gallons of pure water.
Incoming rate of brine solution is = 3 gal/min. and it has quantity 4 pounds/gal.
Outgoing rate of mixed solution = 6 gal/min.
A(t) denotes the number of salt (pounds ) in the tank at time t.
The model can be written as ,
Therefore the differentiation equation becomes ,
with initial conditions A(0)=0 .
Or,
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