A bicycle with 19-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. The cyclist pedals at 180 rpm.

Question

The linear speed of the bicycle in inches per minute =  in/min

The speed of the bike in miles per hour =  mph

Answer 1

The rear sprocket (and therefore the rear wheel) will rotate at 7*180/4 rpm.

Each wheel revolution will be 19π inches.

Therefore the speed in in/min will be 7*180*19π/4

Multiply this by (60 min/hr)*(1 ft/12 in) * (1 mi/5280) to get mph.