## 287. Math Puzzle $4 / 89$

Jakob lives in Adorf but goes to school in Bedorf. In the summer, he often walks the way home through the forest. From the edge of the forest, he can always see his house.

Quite often, his dog Putzi sits in front of the door, ready to take off as soon as he sees Jakob, to greet him. After the first joyful reunion, Putzi races back to the house, makes an immediate U-turn, and rushes back to Jakob, barking with joy, until they finally arrive at the door together.

What distance does the lively dog cover if we know that the house is 1 km from the edge of the forest, Jakob walks at a pace of $5 \mathrm{~km} / \mathrm{h}$, and Putzi moves his four paws at $15 \mathrm{~km} / \mathrm{h}$ over the distance?
The lively Putzi runs for as long as his owner Jakob, but he is three times as fast. Therefore, the four-legged one covers three times the distance: $3 \mathrm{~km}$.