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MathNet 2024-part-04 — 168 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2024-part-04 — 168 problems (EN–VI)

Question 25

Pjotr has a bath with a stopper in the bottom that he can fill with two identical taps. The water flows out of both taps at the same constant speed, and the bath empties (if the stopper is not there) at a constant speed. On Monday, Pjotr fills the bathtub to the brim by turning one tap fully open, then pulls out the stopper and waits for the bathtub to empty again. Only when the bath is empty does he turn the tap off again. On Tuesday, he fills the bath to the brim by turning both taps fully open, after which he pulls out the stopper and waits for the bath to empty again. Only when the bath is empty does he turn the taps off again. On both days, Pjotr spent exactly 45 minutes from opening the tap/taps to closing them again. How many minutes does it take to completely empty a full bath when both taps are off?