A swimming pool holding 3, 000, 000 gallons has been contaminated with 120, 000 pounds of raw sewage. Pure water is pumped into the swimming pool at a rate of 200 thousand per hour and contaminated water is pumped from the pool at the same rate. gallons The differential equation that models this situation is dS dt a) Solve the differential equation (Show work) 200S == ,S(0) = 120 where S is thousands of pounds of raw sewage and t is hours. 3000 b) People can safely swim in the pool when the amount of raw sewage in the pool is less than 100 pounds. Will you be able to allow swimmers in the pool after 5 hours? (Explain) c) After how many hours will you be able to allow swimmers in the pool? (Explain)