If a drive gear with 40 teeth is turning at 200 RPM, how fast is a driven gear with 25 teeth turning?

To determine the speed of the driven gear, you can use the principle of gear ratios, which relates the number of teeth on the gears to their respective speeds. The gear ratio is determined by the formula:

[ \text{Gear Ratio} = \frac{\text{Teeth on Driven Gear}}{\text{Teeth on Drive Gear}} ]

In this case, the drive gear has 40 teeth and the driven gear has 25 teeth. The ratio of the teeth can be calculated as follows:

[ \text{Gear Ratio} = \frac{25}{40} = 0.625 ]

Now, since the drive gear is turning at 200 RPM, you can find the speed of the driven gear using the formula:

[ \text{Speed of Driven Gear} = \text{Speed of Drive Gear} \times \left( \frac{\text{Teeth on Drive Gear}}{\text{Teeth on Driven Gear}} \right) ]

Plugging in the values:

[ \text{Speed of Driven Gear} = 200 , \text{RPM} \times \left( \frac{40}{25} \right) ]

[ \text{Speed of Driven Gear} =