A child pedaling a bicycle with 33-cm diameter tires notices that the bike moves forward 1.9 m with each cycle of pedaling.If the front gear has 22 teeth,how many teeth does the back gear have?
A)6
B)12
C)24
D)55
E)127

Question

Quizplus · Accepted Answer

The distance the bike moves per pedal cycle is equal to the circumference of the tire times the gear ratio. The circumference of the tire is π times the diameter, which is 33 cm or 0.33 m. So, the circumference is π * 0.33 m. The gear ratio is the number of teeth on the front gear divided by the number of teeth on the back gear. Setting up the equation: 1.9 m = (π * 0.33 m) * (22 / back gear teeth). Solving for the back gear teeth gives approximately 12.

A Child Pedaling a Bicycle with 33-Cm Diameter Tires Notices