## 8. Cyclist and Pedestrian

A cyclist and a pedestrian, 1 km apart, start moving towards each other at the same time. The cyclist travels 300 meters per minute, and the pedestrian travels 90 meters per minute. How far apart will they be 1 minute and 48 seconds after they start?

Result: $\quad 298$
## First solution.

The cyclist and the pedestrian are $1 \mathrm{~km}=1000 \mathrm{~m}$ apart. From this distance, we will subtract the number of meters the cyclist and pedestrian travel in 1 minute and 48 seconds $=108$ seconds.

The cyclist travels 300 meters in 60 seconds, so we conclude that the cyclist travels 5 meters in 1 second.

Therefore, in 108 seconds, the cyclist travels $5 \cdot 108=540$ meters.

The pedestrian travels 90 meters in 60 seconds, so we conclude that the pedestrian travels 3 meters in 2 seconds.

Since $108: 2=54$, in 108 seconds, the pedestrian travels $3 \cdot 54=162$ meters.

Together, the cyclist and the pedestrian have traveled $540+162=702$ meters.

Finally, the distance between the cyclist and the pedestrian is 1000 - $702=298$ meters.