If an 80 tooth gear turns at 250 rpm, what is the rpm of a 120 tooth gear it is meshed with?

The relationship between the rpm of gears that are meshed together is determined by the number of teeth on each gear. When two gears are engaged, the product of the gear's speed (in rpm) and the number of teeth on the gear must remain constant across both gears. This can be captured in the formula:

Gear A teeth * Gear A rpm = Gear B teeth * Gear B rpm

In this scenario, we have an 80-tooth gear turning at 250 rpm. We need to find the rpm of a 120-tooth gear, so we can set up the equation:

80 teeth * 250 rpm = 120 teeth * Gear B rpm

By solving for the rpm of the Gear B:

1. Multiply: 80 teeth * 250 rpm = 20,000

2. Set up the equation: 20,000 = 120 teeth * Gear B rpm

3. Divide both sides by 120 teeth: Gear B rpm = 20,000 / 120

4. Calculate: Gear B rpm = 166.66...

Rounding this value leads to 166.6 rpm. Thus, the rpm of the 120-tooth gear is correctly calculated as 166.6 rpm, affirm