In a bicycle, the radius of the chain wheel is double that of the free wheel. The radius of the rear wheel is 42 cm. What will be the speed of the bicycle if the rider is paddling the bicycle at a rate 35 rotations/min?

Let the radius of the free wheel = r

The radius of the chain wheel = 2r

The chain wheel makes 35 rotations in one minute.

⇒ The free wheel takes 70 rotations in one minute.

The distance covered by the rear wheel in one rotation = 2πr
= $\frac{2\times 22\times 42}{7}=264 cm$ 

In 70 rotations, the distance covered by the rear wheel = 18480 cm

Speed = 18480 cm/min

= $\frac{18480\times 60}{100000}$

= 11.088 km/h