A large mixing tank initially contains 240 gallons of water

A large mixing tank initially contains 240 gallons of water in which 24 pounds of salt is dissolved. Pure water is pumped into the tank at a rate of 2 gal/min. The salt water in the tank is always well stirred. The salt water is pumped out of the tank at a rate of 2 gal/min. Write the differential equation for the amount of salt A(t), in pounds, in the tank at time t, assuming the tank does not overflow.

Solution

Incoming rate is 2 gal/min

OUtgoing rate is 2 gal/min

SO volume of solution remains unchanged at 240 gallons

Let, dA be increase in A in time interval t to t+dt

So,

dA=-(A/240)2dt

dA/dt=-A/120