After the hands of a correct clock coincide, how many minutes pass before they coincide again?

Explanation

1. 01

   The minute hand has to gain a full $360^\circ$ on the hour hand.

2. 02

   It gains $5.5^\circ$ per minute, so time $= 360 \div 5.5 = \frac{720}{11} = 65\frac{5}{11}$ minutes.