Maths Olympiad Prep

Library / /11 of 17

Algebra Difficulty 2.8 Junior Find the answer Netherlands

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 00:00:0000 : 00 : 00 is at midnight, just like an ordinary clock. At a given moment, such an alternative clock reads 10:10:1010 : 10 : 10.
What time (hh : mm : ss) is displayed on an ordinary digital clock at that moment?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

16:13:3016 : 13 : 30

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.