Problem 4.8. The figure shows a road map between the houses of five children. The shortest distance by road from Asya to Galia is 12 km, from Galia to Borya - 10 km, from Asya to Borya 8 km, from Dasha to Galia - 15 km, from Vasya to Galia - 17 km. How many kilometers is the shortest distance by road from Dasha to Vasya?

![](https://cdn.mathpix.com/cropped/2024_05_06_df4c0436ab68970fab15g-07.jpg?height=531&width=872&top_left_y=1073&top_left_x=291)
Answer: 18.

Solution. Add the distances from Dasha to Gala and from Vasya to Gala: $15+17=32$. This will include the "main" road (from Dasha to Vasya) and twice the "branch" from it to Gala.

Add the distance from Asey to Bory to the obtained sum: $32+8=40$. Now all three branches (to Gala - twice) and the main road will be counted, with the segment of the main road between the first and third branches being counted twice.

Subtract the two remaining distances from the obtained value: from Asey to Gala and from Gala to Bory: $40-12-10=18$. Now only the main road will be counted.

## 5th grade