Question

A 36-tooth gear turns three times. It is connected to a 12-tooth gear. How many times does the 12-tooth gear turn?

Answer 1

`9` times

Explanation:

The gear ratio of meshed gears is in the inverse ratio of their teeth.

So the gear ratio of the 12-tooth gear to the 36-tooth gear is

`36 : 12 = 3:1`

To understand this, if the 12-tooth gear turns once, 12 teeth pass the point where the gears mesh.
Therefore 12 teeth on the 36-tooth gear also pass that point.

But 12 teeth on the 36-tooth gear is `12/36 =1/3` of a turn.

So for every turn of the 12-tooth gear the large gear rotates `1/3` turn, and for 3 turns of the small gear the large gear turns once.

If the large gear turns 3 times the small gear turns `3 * 3 = 9` times.