Problem 9.4. Foma and Yerema were traveling to Moscow on a cart at a constant speed along a straight road.

- At 12:00, Foma asked: "How many versts to Moscow?"
- Yerema answered: "82".
- At 13:00, Foma asked: "How many versts to Moscow?"
- Yerema answered: "71".
- At 15:00, Foma asked: "How many versts to Moscow?"
- Yerema answered: "46".

It is known that Yerema rounded the distance to the nearest whole number each time, and if there were two such numbers, he chose either one at his discretion.

At 16:00, Foma asked again: "How many versts to Moscow?" This time, Yerema gave an exact answer without rounding it. What did Yerema answer?
Answer: 34.5 versts.

Solution. From Yeremy's answers, we understand that

- at 12:00, the distance to Moscow was between 81.5 and 88.5 versts;

![](https://cdn.mathpix.com/cropped/2024_05_06_f585fb32d0f8951822d4g-5.jpg?height=47&width=757&top_left_y=162&top_left_x=146)

- at 15:00, the distance to Moscow was between 45.5 and 46.5 versts. That is, Foma and Yeremy
- from 12:00 to 13:00, they traveled between 10 and 12 versts;
- from 13:00 to 15:00, they traveled between 24 and 26 versts.

Since the speed of the carriage is constant, it is uniquely determined and equals 12 versts per hour (this is the maximum possible speed from 12:00 to 13:00 and the minimum possible speed from 13:00 to 15:00). Additionally, we get that

- at 12:00, the distance to Moscow was 82.5 versts;
- at 13:00, the distance to Moscow was 70.5 versts;

![](https://cdn.mathpix.com/cropped/2024_05_06_f585fb32d0f8951822d4g-5.jpg?height=44&width=612&top_left_y=745&top_left_x=146)

Thus, at 16:00, the distance to Moscow was 34.5 versts.