Salt flows into the tank at a rate of
(1/2 lb/gal) * (6 gal/min) = 3 lb/min
and flows out at a rate of
(Q(t)/60 lb/gal) * (6 gal/min) = 6Q(t) lb/min
The net rate of change of the amount of salt in the tank at time is then governed by
Solve for :
The tank starts with 10 lb of salt, so that Q(0) = 10. This gives us
so that the amount of salt in the tank at time is given by