14. (3 points) There is a clock that now shows 10 o'clock. After $\qquad$ minutes, the minute hand and the hour hand overlap for the first time; after another $\qquad$ minutes, the minute hand and the hour hand overlap for the second time.
14. (3 points) There is a clock now showing 10 o'clock. After $\frac{54}{11}$ minutes, the minute hand and the hour hand overlap for the first time; after another $65 \frac{5}{11}$ _minutes, the minute hand and the hour hand overlap for the second time.
【Solution】Let $x$ be the number of minutes after 10 o'clock when the two hands overlap. According to the problem, we have:
$$
x-\frac{5}{60} x=50 \text {, }
$$

Solving this equation gives: $x=54 \frac{6}{11}$;
Let $y$ be the number of minutes after the first overlap when the two hands overlap again. According to the problem, we have:
$$
y-\frac{5}{60} y=60 \text {, }
$$

Solving this equation gives: $y=65 \frac{5}{11}$.
Therefore, the answers are: $54 \frac{6}{11} ; 65 \frac{5}{11}$.