Your swimming pool containing 65,000 gal of water has been contaminated by 7 kg of a nontoxic dye that leaves a swimmer's skin an unattractive green. The pool's filtering system can take water from the pool, remove the dye, and return the water to the pool at a flow rate of 200 gal/min. Assume that the dye is uniformly distributed throughout the pool.
(a) What is the initial value problem for the filtering process?
(b) You have invited several dozen friends to a pool party that is scheduled to begin in 4 h. You have determined that the effect of the dye is imperceptible if its concentration is less than 0.03 g/gal. Is your filtering system capable of reducing the dye
concentration to this level within 4 h?