13.251. The hour and minute hands coincide at midnight, and a new day begins. At what hour of this new day will the hour and minute hands coincide again for the first time, assuming that the clock hands move without jumps?
## Solution.

Let's assume the speed of the minute hand is 1, then the speed of the hour hand is $-\frac{1}{12} \cdot$ The hands will coincide when $\frac{1}{12} \cdot t + 60 = t$, where $t$ is the time of movement of the hands.

Solving the equation, we find $t = \frac{720}{11}$ (min).

Answer: 1 hr $5 \frac{5}{11}$ min.