Differential Equations · Superchallenge problem

A tank contains $100$ L of brine holding $20$ kg of dissolved salt. Brine with concentration $0.5$ kg/L flows in at $3$ L/min while the well-mixed solution drains out at only $2$ L/min (so the volume increases). Find the salt content, in kg, at the moment the tank holds exactly $150$ L. Give an exact fraction.