How fast is the bike moving in mph (to two decimal places)

Question

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 3-in. radius on the rear sprocket. The cyclist pedals at 190 rpm.

a) Find the linear speed of the bicycle in in/min (correct to at least two decimal places)



b) How fast is the bike moving in mph (to two decimal places)

Answer 1

For every revolution of the 7" sprocket, the 3" sprocket makes 7/3 revolution.

190 rpm (7/3) = 443 1/3 revolutions

19π" (433 1/3) ≈ 26,462.681"

26,462.681" / (12")(5280') ≈ 0.418 mph