What time is it that the long hand overlaps with the hour hand between 2:00 and 3:00?
Because the long hand goes ahead 360° for one hour (60 minutes), it goes ahead 360°/60=6 degrees in one minute.
Because the hour hand goes ahead one clockface = 30 degrees for one hour, it goes ahead 30°/60=0.5 degrees in one minute.
When the long hand runs after the hour hand, the angle between the both hands is shortened by 6° - 0.5°= 5.5 degrees in one minute.
The long hand was behind the hour hand by 60 degrees at 2:00 and the time the long hand catches up with the hour hand by moving 60 degrees more than the hour hand is calculated by 60° / 5.5° = 120/11 minutes.
Answer
2 o’clock 120/11 minutes
Solution
An angle of the long hand and the hour hand is 30° × 2 = 60 degrees at 2:00 and the long hand will move after the hour hand.
Because the long hand goes ahead 360° for one hour (60 minutes), it goes ahead 360°/60=6 degrees in one minute.
Because the hour hand goes ahead one clockface = 30 degrees for one hour, it goes ahead 30°/60=0.5 degrees in one minute.
When the long hand runs after the hour hand, the angle between the both hands is shortened by 6° - 0.5°= 5.5 degrees in one minute.
The long hand was behind the hour hand by 60 degrees at 2:00 and the time the long hand catches up with the hour hand by moving 60 degrees more than the hour hand is calculated by 60° / 5.5° = 120/11 minutes.
