A gallon tank initially contains 500 gallons of water with 4 lbs of salt dissolved in it. Water enters the tank at a rate of 8 gal/hr and the water entering the tank has a concentration of (1/3) lbs/gal.

a) If a well mixed solution leaves the tank at a rate of 8 gal/hr and the volume of water is the same, what is the quantity of salt at time t?

b) If a well mixed solution leaves the tank at a rate of 6 gal/hr (so the volume of water is not necessarily the same), what is the differential equation satisfied by the amount of salt Q(t) at time t? The volume of water in the tank depends now on t.

I primarily need help with part (b), but an answer to (a) would be fine so I may double check my answer.