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_2fdcf97aa9799d0d4cd6g-07.jpg?height=531&width=872&top_left_y=1073&top_left_x=291)
Answer: 18.

Solution. Let's 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.

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

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

## 5th grade