# If you have a gear train with two gears, one with 40 teeth and the other with 4 teeth, how many revolutions does the second gear make for each revolution of the first gear?

10

Explanation

The gear ratio $$({V_r})$$ of a gear train is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

$$\left.V_{r}=\frac{N_{1}}{N_{2}}\right)\left(\frac{N_{2}}{N_{3}}\right)\left(\frac{N_{3}}{N_{4}}\right) \ldots\left(\frac{N_{n}}{N_{n+1}}\right)$$
In this problem, we have only two gears so the equation becomes:

$$V_{r}=\frac{N_{1}}{N_{2}}=\frac{40}{4}=10$$