The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second.

The question should be "Find the speed of the bicycle in feet per second and miles per hour."

4-inch pedal sprocket rotates at 1 rev/sec

2-inch wheel sprocket rotates at twice the rate of the pedal sprocket=2 rev/sec

14 inch wheel rotates 2/14=1/7 the rate of the wheel sprocket=2/7 rev/sec

inches and rev cancel out

(2/7) (28pi) / 12=8pi/12=2pi/3=2.09 ft/sec

sec and ft cancel out

2pi*3600/3*5280=1.42 mi/hr

...

speed of the bicycle=2.09 ft/sec or 1.42 mi/hr