A gear with 25 teeth turning at 500 RPM drives a gear with how many teeth if the driven gear turns at 166.66 RPM?

To determine the number of teeth on the driven gear, you can use the relationship between the gears' speeds and the number of teeth. This is based on the principle that the product of the speed (RPM) and the number of teeth on a gear remains constant when two gears are engaged.

In this case, we know:

• The driving gear has 25 teeth and is turning at 500 RPM.

• The driven gear's speed is 166.66 RPM.

The formula to find the relationship between the gears is:

[

\text{Teeth of Driver Gear} \times \text{RPM of Driver Gear} = \text{Teeth of Driven Gear} \times \text{RPM of Driven Gear}

]

Substituting the known values into the equation gives:

[

25 \text{ teeth} \times 500 \text{ RPM} = \text{Teeth of Driven Gear} \times 166.66 \text{ RPM}

]

Calculating the left side:

[

25 \times 500 = 12500

]

Now, dividing both sides of the equation by 166.66 RPM to find the number of teeth on the driven gear:

[

\text{Te