Night Watchmen
Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?
Age
11 to 14
Challenge level
Problem
Granny'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?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 12 noon (assuming 12 hour analogue watches. 24 hour watches won't agree again until midnight tomorrow, when they will both say midday)
| Time | Granny | Grandpa | Difference |
| 00:00 | 00:00 | 00:00 | 0 |
| 01:00 | 01:30 | 00:30 | 1 |
| 02:00 | 03:00 | 01:00 | 2 |
| 03:00 | 04:30 | 01:30 | 3 |
+1 hour apart each hour
12 hours apart after 12 hours
They say the same time at 12 noon (6 o'clock)