The speed of a gear is governed by the number of teeth on the gear. When a smaller gear is driving a larger one, the smaller gear must rotate more times in order for the larger one to rotate once. For example, if the smaller gear (driving gear) has 20 teeth and the larger one has 40 teeth, the smaller one must rotate twice for the larger one to rotate once.
This is because as the smaller gear rotates, its teeth must push the teeth of the larger gear to make it rotate. Because there are more teeth on the larger gear, it takes more teeth from the smaller gear to make it rotate once.
Therefore, if the driving is smaller than driven gear, the driven gear turns faster.
