Question

A large tank holds 300 gallons of a brine solution. Salt was entering and leaving the tank; a brine solutions was being pumped into the tank at the rate of 3 gal/min; it mixed with the solution there, and the mixture was then pumped out at a rate of 2 gal/min so the liquid is accumulating at a rate of 1gal/min. The concentration of salt in the inflow was 2 lb/gal  salt was entering at the rate of (2 lb/gal) . (3 gal/min) = 6 lb/min.  

If 50 lbs of salt were dissolved initially in the 300 gallons.

Rate in - Rate out = 1 gal/min

After t mins, (1 gal/min). (t min) = t gal, will accumulate so the tank will contain 300 + t gallons of brine. The concentration of the outflow is then c(t) = A/(300+t) lb/gal, and the output rate of salt is R out = (A/(300+t)) lb/gal . (2 gal/min) = 2A/(300+t) lb/min.

Solve dA/dt + 2A/(300+t) = 6 using Laplace transformation and show your workings (including the inverse Laplace transformations).

Answer 1