Why gears change speed and direction
Pro-Tip. Fewer teeth, faster spin. The other gear turns the opposite way.
Gear teeth have to fit together. When one tooth pushes the next, the two wheels turn opposite ways. If the driver turns clockwise, the gear it drives turns counterclockwise.
They pass the same number of teeth each minute. Teeth times RPM on one gear equals teeth times RPM on the other. The number in the center of the drawing is the tooth count.
Fewer teeth means a smaller wheel and a faster spin. A 48-tooth gear driving a 16-tooth gear turns the small one 48 รท 16 = 3 times as fast. A bigger drawing is not the faster gear.
Worked example
The 48-tooth driver turns at 20 RPM.
The 16-tooth gear turns at 60 RPM, the other way.