Please explain me this Problem What is the solution In Class

Please explain me this Problem. What is the solution?

In Class Problem: The time is now twelve o\'clock noon. When is the next time that the minute hand and the hour hand of the clock will overlap? Assume that the minute and hour hands move continuously (a opposed to ticking) and each moves at its own constant rate.

Solution

Solution: The overlap will happen 11 times in a 12 hour period.

Thus first overlap at = 12/11 = 1.09090...

                                     =65.454545...minute

                                     = 1 hour 5 minute 27.2727.. second

Therefore next time hour hand overlap the minute hand at about 1:05:27 o\'clock noon.