## Task 3 - 260613

The connecting roads of three places $A, B, C$ form a triangle. In the middle of the road from $B$ to $C$ lies another place $D$. The distance from $A$ via $B$ to $C$ is $25 \mathrm{~km}$, from $B$ via $C$ to $A$ is $27 \mathrm{~km}$, and from $C$ via $A$ to $B$ is $28 \mathrm{~km}$.

A pioneer group hikes on the mentioned roads from place $A$ to place $D$ via the shortest route.

a) Through which of the two places $B$ or $C$ does the pioneer group pass?

Justify your decision!

b) How much time does she save compared to the longer of the two possible routes from $A$ to $D$ if she travels $4 \mathrm{~km}$ per hour?

c) How long is the total distance she has traveled?