A perfectly mixed stirred$-$tank containing $100kg$ of water initially is further filled with $150kg$

of water and $30kg$ of salt per hour, while the solution is taken out at a rate of $120kg$ per

hour. Assuming a complete mixing:

a$.$ Model a differential equation that describes the time rate of change of total mass in

the tank.

b$.$ Determine the amount of salt in the tank at $9$ mins.