The Mad Hatter's Watch
Weekly Problem 35 - 2013
The hour hand on the Mad Hatter's watch moves normally, but the minute hand moves too fast! When will it next show the correct time?
The hour hand on the Mad Hatter's watch moves normally, but the minute hand moves too fast! When will it next show the correct time?
Age
11 to 14
Challenge level
Problem
The hour hand on the Mad Hatter's watch moves at the correct speed, but the minute hand moves one and a half times as fast as it should. Yesterday, it showed the correct time at 3 p.m. When did it next show the correct time?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The watch will show the correct time when the minute hand is next in the correct position. The minute hand gains half a minute every minute on the correct time. It will show the correct time when it has gained an hour.
This will take two hours, so the next correct time will be at 5pm.