let = the angular speed of the pedal gear in radians/unit time.

= the angular speed of the rear gear in radians/unit time

= pedal gear radius

= rear gear radius

= rear wheel radius

since the chain connecting the pedal gear to the rear gear moves over each gear at the same linear speed ...

... the front to rear gear ratio.

the rear wheel and rear gear spin at the same angular rate ... the linear speed that the rear wheel spins (and the bike travels) is

so ...