A bath tub can be filled by the cold water pipe in 9 minutes and by the hot water pipe in 11.25 minutes. A person left the bathroom after turning on both the pipes simultaneously and returned at the moment when the bath tub should be full. Finding that the waste pipe had been left open, he closed it. In 3.75 minutes more, the bath tub was full. In what time would the waste pipe empty it?

Combined fill rate of cold and hot pipes: 1/9 + 1/11.25 = 1/5 tub per minute. In 5 minutes, tub would be full if no waste pipe. After closing waste pipe, it took 3.75 minutes more to fill, meaning only 0.75 of tub was filled in those 3.75 minutes at rate 0.2 per minute. So waste pipe had drained 0.25 of tub in 5 minutes. Drain rate = 0.25/5 = 1/20 per minute. Time to empty full tub = 20 minutes. Wait - let me recalculate: fill rate is 1/5 per minute = 0.2. In 3.75 minutes after closing waste, amount filled = 3.75 × 0.2 = 0.75. So when waste was closed, 0.25 was filled. Waste pipe drained for 5 minutes and removed 0.75 of tub. Drain rate = 0.75/5 = 0.15 per minute. Time to empty = 1/0.15 = 6.67 minutes.