## 2. Ante and Borna

Ante started from place $A$ to place $B$, and Borna started from place $B$ to place $A$ along the same route. After Ante had walked one-third of the total distance plus $107 \mathrm{~km}$, and Borna had walked one-sixth of the total distance plus $161 \mathrm{~km}$, their mutual distance was $113 \mathrm{~km}$. What is the distance, in kilometers, between places $A$ and $B$ if Ante and Borna have not yet passed each other?

Result:
Solution.

Ante crossed

![](https://cdn.mathpix.com/cropped/2024_05_30_d078161e0adaef934ec1g-2.jpg?height=246&width=742&top_left_y=128&top_left_x=497)

Borna crossed

![](https://cdn.mathpix.com/cropped/2024_05_30_d078161e0adaef934ec1g-2.jpg?height=262&width=740&top_left_y=380&top_left_x=498)

After that, their mutual distance is $113 \mathrm{~km}$

![](https://cdn.mathpix.com/cropped/2024_05_30_d078161e0adaef934ec1g-2.jpg?height=268&width=742&top_left_y=737&top_left_x=514)

so the sum of the distances $107+113+161=381 \mathrm{~km}$ is equal to half the total length of the road.

Therefore, the distance between place A and B is $2 \cdot 381=762 \mathrm{~km}$.