Out of sync
Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?
Age
11 to 14
Challenge level
Problem
Albert Einstein was standing on the station platform thinking about relativity when he noticed that he could see two station clocks. Each clock was digital, showing only hours and minutes.
He observed that the display on one clock changed to the next minute $10$ seconds before the correct time, whereas the display on the other clock changed to the next minute $10$ seconds after the correct time.
For what fraction of the day did the clocks show the same time?
Student Solutions
Answer: $\frac23$
In each minute, the two clocks showed the same time for $40$ seconds, i.e. they showed the same time for ${40\over60} = {2\over3}$ of the day.