35.2. Two motorcyclists set out simultaneously from points $A$ and $B$ towards each other and met 50 km from $B$. Upon arriving at points $A$ and $B$, the motorcyclists immediately turned around and met again 25 km from $A$. How many kilometers is it from $A$ to $B$?
35.2. Let the motorcyclists meet for the first time at point $C$, and for the second time at point $D$ (Fig. 19). Then $B C=50$ km and $A D=25$ km.

![](https://cdn.mathpix.com/cropped/2024_05_21_f0d089db3d527e92a992g-32.jpg?height=166&width=916&top_left_y=1179&top_left_x=570)

Fig. 19

Let $A B=x$ km. Clearly, before the first meeting, the motorcyclists traveled $x$ km, and before the second meeting, they traveled $3 x$ km, i.e., three times more. Therefore, before the second meeting, each motorcyclist traveled three times the distance they traveled before the first meeting. Since the second motorcyclist traveled 50 km before the first meeting, he traveled 150 km before the second meeting. On the other hand, it is easy to see that before the second meeting, the second motorcyclist traveled $(x+25)$ km. Thus, we have the equation: $x+25=150$, from which $x=125$, i.e., $A B=125$ km.