- The cyclist pedals at rpm.
- The ratio of the number of teeth on the front gear to the rear gear is .
- The diameter of the rear wheel is metres,
So in one minute, the pedals, and therefore the front gear, complete revolutions. Since the gear ratio is , the rear gear will need to complete revolutions for every one revolution that the front gear makes. This is because the number of gear teeth that move by a fixed point must be the same at the front and rear. So the rear gear - and hence the rear wheel - makes revolutions in one minute.
Now if the diameter of the rear wheel is metres, its circumference is metres, which is, of course, the distance the cycle will move forward in one revolution of the rear wheel. So the total distance that it moves in one minute is metres. If we divide by 60, that will give us a speed of
metres per second.