A 21​-tooth gear on a motor shaft drives a larger gear having 70 teeth. If the motor shaft rotates at 1000 ​rpm, what is the speed of the larger​ gear? The speed of the larger gear is nothing rpm.

Question

This is for applied business math.

Answer 1

The gear ratio is 70:21 or 70/21=10/3.

The ratio of the speeds should be the same as the inverse ratio of the gears.

With every 10 rotations of the smaller gear (with fewer teeth) the larger gear only rotates 3 times, because 10×21=3×70=210 teeth as the teeth engage.

So with every 1000 rotations of the smaller gear, the larger gear rotates 300 times, making the speed of the larger gear 300rpm.