A bicycle with 20-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 115 rpm.

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

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

Question

A bicycle with 20-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 115 rpm.

Find the linear speed of the bicycle in in/min (correct to two decimal places).       in/min

How fast is the bike moving in mph (to two decimal places)?       mph

whpalmer4 · Answer

One rotation of the front sprocket causes 7/3 rotations of the rear sprocket and thus the rear wheel.  The bicycle travels $\pi d$ units forward for each forward rotation of the rear wheel.

The gear ratio and pedaling rates are plausible, but the radii of the sprockets are not likely, especially on a bike with 20” wheels!