Question

A tank initially contains 50 gal of fresh water. At t = 0, brine solution containing 2 lb of salt per gallon is poured into the tank at the rate of 12 gal/min, while the well stirred mixture leaves the tank at the rate of 8 gal/min. What is the amount of the salt at the end of minutes? How long it will take to obtain an amount of 50 lb?

Answer 1

$$\frac{ds}{dt}=24-\frac{8s}{50+4t}\\t=2.47\ min$$