If the ratio of teeth between two gears is 3:1, how does the speed of the two gears compare?

In a gear system, the relationship between the speeds of the driver and driven gears is inversely proportional to the ratio of the number of teeth on each gear. When the ratio of teeth between two gears is 3:1, it indicates that for every three turns of the driver gear (the gear providing the input motion), the driven gear (the gear receiving the motion) makes one complete turn.

This means that because the driver gear has three times the number of teeth compared to the driven gear, it must rotate faster to keep up with the movement of the driven gear. As a result, the speed of the driver gear is indeed three times that of the driven gear—a clear outcome of the mechanical advantage provided by the difference in tooth count.

Thus, in this case, understanding the principles of gear mechanics allows us to conclude that the driver gear's speed is three times that of the driven gear, confirming the correctness of the given answer.