A200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. a salt solution
with 1/4 pound of salt per gallon is added to the tank at 4 gal/min, and the resulting mixture is
drained out at 2 gal/min. find the quantity of salt in the tank as it’s about to overflow.

Set up a differential equation using rate of salt going in minus rate going out.

Rate = dS/dt = salt/gal* gal/min

Also the number of gallons in tank is increasing at (4-2) gal/min = 2 gal/min
The volume of tank at any given time = 100+2t

Differential Equation:


Use integrating factor of t+50


Integrate both sides

Solve for constant c given S(0) = 20
c = 1000

Tank is full at 200 gallons when t =50
100+2t = 200 ---> t = 50

S(50) = 47.5 

Final There are 47.5 pounds of salt