(A comical aside to the B-kun/Y-san series...a snippet from the past...)
Having won their third consecutive state swim meet, Ecidius University was celebrating by throwing a pool party for the athletes, coaches, and their friends at their brand spanking new new pool (donated by one of their many alums who had more money than they knew what to do with courtesy of the .com era).
Ecidius's star athlete, as well as the indisputable top of his class in academics, B-kun, arrived early in order to get in his daily 100 laps (after having run his daily 10 miles, doing his daily 200 push-ups, and practicing his martial arts and kendo for his daily 2 hours...each).
As he approached, he noticed something strange...the pool water was...purple. He dipped his finger into it, and the hue left a stain on his skin.
He scowled as the lopsidedly smiling face popped into his mind. That woman...
After running some tests with the aid of a few (of many) of his admirers in the chemistry department, he determined that there was 5 kg of dye in the 60,000 gallons of water in the pool. He knew that the pool's filtering system could pump out water, remove the dye, and return the water to the pool at a rate of 200 gallons/min.
The doting chemistry majors had also informed him that the effects of the dye became imperceptible when the concentration came below 0.02 grams/gallon.
The pool party started in 4 hours, but he was slated to deliver a speech before anyone could jump in. How long would his speech need to last for to ensure no guests ended up with purple-tinted skin?