Problem 7.2. Along the road stand the houses of Andrey, Boris, Vasya, and Gena (in that order). The distance between Andrey's and Gena's houses is 2450 meters. One day, the boys decided to have a 1 km race. They set the start halfway between Andrey's and Vasya's houses. As a result, the finish line was exactly halfway between Boris's and Gena's houses. What is the distance from Boris's to Vasya's house? Provide the answer in meters.
Answer: 450.

Solution. Let's assume that the road goes from Andrey's house eastward to Gena's house; then we can say that Gena's house is east of Vasya's house, and Borya's house is east of Andrey's house. This means that the finish (the midpoint between Borya's and Gena's houses) is east of the start (the midpoint between Andrey's and Vasya's houses).

![](https://cdn.mathpix.com/cropped/2024_05_06_c7c94bf2f2dc4a178b54g-1.jpg?height=153&width=713&top_left_y=1470&top_left_x=370)

Fig. 1: to the solution of problem 7.2

Let the start be located $y$ meters east of Andrey's house, then the finish is at a distance of $y+1000$ (Fig. 1). If the distance from Borya's house to Andrey's house is denoted by $b$, then the difference $(y+1000)-b$ is the distance from Borya's house to the finish, and the difference $2450-(y+1000)$ is the distance from Gena's house to the finish. They are equal:

$$
(y+1000)-b=2450-(y+1000)
$$

from which it is not difficult to extract $b=2 y-450$.

On the other hand, the distance from Vasya's house to Andrey's house is $2 y$, since the start is located halfway between them. This means that the distance from Vasya's house to Borya's house is 450.