## 296. Math Puzzle $1 / 90$

Sabine values physical exercise a lot, and so her daily commute to school by bike means more to her than just fulfilling a necessary "evil."

On her route, she has to cross a $100 \mathrm{~m}$ long bridge. One day, she meets a classmate on the bridge after $40 \mathrm{~m}$, who was cycling towards her at the same speed as she was. "Forgot my sports gear," Sabine thought.

A car driver traveling at 70 km/h met one of the girls at the beginning of the bridge and the other at the end of the bridge.

At what speed were the two students cycling?
When the car is driving in Sabine's direction, it first encounters the oncoming cyclist at the beginning of the bridge.

By this time, Sabine has covered $40 \mathrm{~m} + 40 \mathrm{~m} = 80 \mathrm{~m}$.

During the time it takes Sabine to pedal the last $20 \mathrm{~m}$, the car covers the entire length of the bridge - 100 meters - and passes Sabine at the end of the bridge.

The car has five times the speed of the bicycles, which clarifies that the two girls were cycling at $14 \mathrm{~km} / \mathrm{h}$.

In the case of the car reversing direction, the speed ratios would be the same.