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Junior Mathematical Olympiad

Netherlands algebra

Problem

A city wants to conduct a trial with alternative time measurements: a 24-hour day will be divided into 15 howers, an hower into 72 minotes, and a minote again into 80 seconds, which are as long as seconds in ordinary timekeeping. In other words, 15 howers of 72 minotes with 80 seconds last as long as 24 hours of 60 minutes with 60 seconds. In the city, digital clocks are used on which the first two digits indicate howers, the next two indicate minotes and the last two indicate seconds. The time is at midnight, just like an ordinary clock. At a given moment, such an alternative clock reads . What time (hh : mm : ss) is displayed on an ordinary digital clock at that moment?
Solution
Final answer
16 : 13 : 30

Techniques

Fractions