A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure
water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the
concentration of salt in the brine entering the tank is .2 kg/L, determine the mass of salt in the tank after t min.
When will the concentration of salt in the tank reach 0.1 kg/L?

Question

A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure 
 water.  The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min.  If the 
 concentration of salt in the brine entering the tank is .2 kg/L, determine the mass of salt in the tank after t min.  
 When will the concentration of salt in the tank reach 0.1 kg/L?

anonymous · Answer

You'll have to set this up as a differential equation. If Q(t) is the amount of salt in the tank, then the derivative of Q(t) is Q'(t)=.2*4*t-3*(Q(t)/(100+t)). The initial conditions are Q(0) = 0. Once you solve for Q(t) you then need to solve for t in Q(t)/(100+t) = .1.

anonymous · Answer

Sorry, the .2*4*t should instead be just .2*4.