IMC 2007 Q17
17. Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. At midnight, they both set their watches to the correct time of 12 o'clock. What is the correct time when their two watches next agree?
Grannie's watch: 
Grandpa's watch: 
Grandpa's watch: - A 6 am
- B 9 am
- C 12 noon
- D 3 pm
- E 6 pm
Intermediate Mathematical Challenge 2007, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 12 noon
The two watches will next agree when Grannie's watch has gained twelve hours relative to Grandpa's watch. Each hour, Grannie's watch gains one hour relative to Grandpa's watch, so it will take 12 hours for this to happen. At this time, both watches will show a time of 6 o'clock.
Solution © UK Mathematics Trust, from the IMC 2007 solutions.