Please help me with a differential equation word problem involving mixing a salt water solution.

5. Suppose you have a container that contains 500 L of a salt water solution with a concentration of 0.3 kg of salt per liter. Pure water enters the tank at a rate of 7 L/min. The solution is mixed and drains at the same rate. Let S(t) be the amount of salt in the container at time t.

(a) Determine S(0), the initial amount of salt in the container.

(b) The assumption that the solution is mixed implies that the concentration of salt at time t is a constant500S(t)kg (of salt)/L of solution. Use this to determine the flow of salt out of the container in kg/min.

(c) Solve the initial value problem.

(d) Determine the time it will take for the concentration of salt to reach 0.1 kg/L.