When it is 10:00, the hour hand on an analog clock is 300 degrees ahead of the minute hand. How many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?

Answer 1

The hour hand moves 30 degrees per hour, or 0.5 degrees per minute.
The minutes hand moves 360 degrees per hour, or 6 degrees per minute.
The difference between the two is 5.5 degrees per minute.
To catch up with 300 degrees difference, it takes: 300/5.5 minutes = 600/11 = 54 6/11 minutes.