Use differential equations to find the salinity of a solution

We begin with a tank containing 100 gallons of water and 50 pounds of dissolved salt. Pure water is added to the tank at a rate of 3 gallons per minute (the concentration of the salt is kept constant by stirring). If the mixture runs out of the tank at 2 gallons per minute, how much salt (in pounds) is in the tank at the end of 60 minutes?

Let $y = f(t)$ be the number of pounds of salt in the tank at time $t$ . Since water leaving the tank at a rate of 2 gallons per minute, and at time $t$ there are $100 + (3-2)t = 100 + t$ gallons of water in the tank (since water is entering the tank at a rate of 3 gallons per minute) we have

$y' = -2 \left( \frac{y}{100+t} \right).$

(Since $y'$ is the change in the amount of salt at time $t$ and $\frac{y}{100+t}$ is the concentration of salt in the water at time $t$ .) Therefore, we have the first-order differential equation