A tank contains $1400$ L of pure water. A solution that contains $0.06$ kg of sugar per liter enters a tank at the rate $3$ L/min The solution is mixed and drains from the tank at the same rate.

(a) How much sugar is in the tank initially?
(kg)

(b) Find the amount of sugar in the tank after $t$ minutes.
amount = (kg)
(your answer should be a function of $t$)

(c) Find the concentration of sugar in the solution in the tank after $78$ minutes.
concentration = (kg/L)