Your swimming pool containing 65000 gal of water has been contaminated by 6 kg o
ID: 1948104 • Letter: Y
Question
Your swimming pool containing 65000 gal of water has been contaminated by 6 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 water to the pool at a flow rate of 225 gal/min.Find the time T at which the concentration of dye first reaches the value c0 = 0.017 g/gal
these are the possible choices:
T = 486.78 minutes
T = 490.78 minutes
T = 488.78 minutes
T = 492.78 minutes
T = 494.78 minutes
Explanation / Answer
v = volume of the water in the pool = 65 000 gal ; constant m1 = amount of dye at initial moment = 4 000 g ; m variable of time q = recycling flow = 200 gal/min ; constant c1 = initial concentration of dye = m1/v = 0.0615 g/gal c0 = needed concentration = 0.017 g/gal c(t) = m1 * (1-qt/v) / v ; at any moment t so we need time t0 when c = c0 ==> 1 - qt0 / v = c0 * v / m1 ==> qt0 / v = 1 - c0 * v / m1 ==> t0 = v (1 - c0 * v / m1) / q = 65000 * (1-0.017*65000/4000) / 200 = 486.78 min
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.