## 240. Math Puzzle $5 / 85$

Ralf went on a bike ride with his friend to a lake 20 km away. Their front chainrings have 46 teeth, and the rear ones have 16.

The diameters of their rear wheels are 70 cm. In the evening, they rode back.

How many times did each of them have to pedal if the freewheel was not used and wind resistance is neglected? $(\pi=3.1416)$
They drive $40 \mathrm{~km}$ back and forth.

With one revolution of the front sprocket, the rear wheel rolls $\frac{46}{16} \cdot 0.7 \cdot \pi = 6.32247 \mathrm{~m}$.

$$
\frac{40000}{6.32247} = \frac{40000 \cdot 16}{46 \cdot 0.7 \cdot 3.1416} = 6326.6 \text { revolutions }
$$

Each of them had to pedal 6327 times on this 40-km ride.