## 4. The Hound and the Fox

The hound spots a fox 123 meters away and rushes after it. The fox runs ahead of the hound, and both move in the same direction. Each hound's leap is 2 meters long, and each fox's leap is 1 meter. While the hound jumps twice, the fox jumps three times. At what distance from its starting point does the hound catch the fox?

## Result: $\quad 492$
## First solution.

For every two jumps of 2 meters, the dog jumps 4 meters, while at the same time, with three jumps, the fox jumps 3 meters, and the distance between them decreases by 1 meter.

While the dog jumps 123 times in sets of 2 jumps and covers $123 \cdot 2 \cdot 2=492 \mathrm{~m}$, the fox will, in the same time, jump 123 times in sets of 3 jumps and cover $123 \cdot 3 \cdot 1=369 \mathrm{~m}$.

Since the fox was ahead of the dog by 123 meters, the dog will catch up to the fox at a distance of 492 meters from the starting point.