Math Exploration: Clock Hands Problem

The Problem: At 12:00:00, the hour and the minute hands of a clock coincide. How much time passes before the next instant that the hour and minute hands coincide?

My solution:
The minute and hour hand will collide again after one but before two complete revolutions of the minute hand.

Let x be the number of minutes the hour hand travels and t be the amount of time until they next coincide.

Then 60+x is the number of minutes the minute hand travels.

The minute hand travels at a rate of 1 (in terms of minutes passed).

The hour hand travels at a rate of 5/60 = 1/12 (since it is on the 5 minute mark after 60 minutes).

Since distance = speed*time
x = (1/12)t
60 + x = t
Therefore,

60 + (1/12)t = t
60 = (11/12)t
60*(12/11) = t

Since this is in minutes, we have to divide by 60 to get hours.

t=12/11

It takes 12/11 hours for the clock hands to next coincide. In other words, it takes 1 hour, 5 minutes and 27+27/99 seconds.