7.2. One morning at 9:00, pedestrian Fedia left the village of Fedino for the village of Novoverandovo. At the same time, cyclist Vera set off towards him from Novoverandovo. It is known that by the time they met, Fedia had walked one-third of the distance between the villages. However, if Fedia had left an hour earlier, he would have walked half the distance by the time they met. At what time did Fedia and Vera meet? The speeds of Vera and Fedia are constant.
Answer: $10: 20$

Solution 1: Understand that if Fedya has walked some distance before Vera sets off, then from the moment Vera starts until they meet, he will walk a third of the remaining distance. This means that the midpoint of the entire distance is a third of the remaining distance, so Fedya covers one quarter of the total distance in one hour. From the first condition, it is clear that Vera's speed is twice as fast, meaning Fedya and Vera together cover $3 / 4$ of the distance in one hour, so they will need $4 / 3$ hours to meet.

Solution 2: Let Fedya's speed be $U$, Vera's speed be $V$, and the distance between the villages be 1. Then from the first condition, we get $V=2 U$.

The second condition can be interpreted as follows: Fedya first walks for 1 hour at speed $U$, and then for $(1-U):(U+V)$ hours at the same speed $U$ (the distance divided by the closing speed), and in total he covers $1 / 2$ of the distance. Therefore, $U+U(1-U):(U+V)=1 / 2$, from which $U=1 / 4$, and then proceed as in the first solution.

Criteria: only the answer, the answer with verification - 1 point.

Getting that $V=2 U$ - another point.

Finding that in one hour the two together cover $3 / 4$ of the distance, with no further progress - 5 points.