Hi Arrayeli H.,
If the pedal sprocket has a 6in radius, it's circumference is 2π(6in) = 12π in., and the rear wheel sprocket is 2π(3in) = 6π in. And 12π/6π = 2, which means that for every 1 revolution the pedal sprocket turns, 2 revolutions of the rear wheel sprocket turns, and thus 2 revolutions of the rear wheel. If the cyclist turns the pedal sprocket at 185 rpm, then the rear wheel will will turn at twice that or 370 rpm.
We can use this 370 rpm of the rear wheel to find the linear speed. The circumference of the rear wheel is πd = 20π, so 1 revolution of the rear wheel equals 20π in linear. (1 rev = 20π in.)
(a) 370 rev/min*(20π in./1 rev) = 7400π in./min or 23247.79 in./min.
(b) 7400π in./min*(60 min/ 1 hour)*(1 ft./12 in.)*(1 mile/ 5280 ft.) = 22.01 mi/hr (mph)
I hope this helps, Joe.
