# If you have a gear train with three gears, the first with 28 teeth, the second with 16 teeth and the third with 8 teeth what is its mechanical advantage?

3.50

Explanation

The mechanical advantage of a gear train is its gear ratio. The gear ratio ${ ({V_r}) }$ is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:
$$V_{T}=\left(\frac{N_{1}}{N_{2}}\right)\left(\frac{N_{2}}{N_{3}}\right)\left(\frac{N_{3}}{N_{4}}\right) \ldots\left(\frac{N_{n}}{N_{n+1}}\right)$$
In this problem, we have three gears so the equation becomes:
$$V_{T}=\left(\frac{N_{1}}{N_{2}}\right)\left(\frac{N_{2}}{N_{3}}\right)=\left(\frac{28}{16}\right)\left(\frac{16}{8}\right)=\frac{28}{8}=3.50$$