Question

) The sprocket assembly on a bicycle consists of a chain and two sprockets, one on the pedal and the other on the rear wheel. If the sprocket on the pedal is 6 inches in diameter, the sprocket on the rear wheel is 4 inches in diameter, and the rear wheel is 26 inches in diameter, how fast is the bicycle traveling in miles per hour when the cyclist is pedaling at the rate of 1.1 revolutions per second? Round your answer to the nearest tenth mph.

Answer 1

Answer:

7.8 mph

Explanation:

Rate of cycling = 1.1 rev/s

Rear wheel diameter = 26 inches

Diameter of sprocket on pedal = 6 inches

Diameter of sprocket on rear wheel = 4 inches

Circumference of rear wheel =  $\pi d=26\pi$

Speed would be

$\text{Rate of cycling}\times \frac{\text{Diameter of sprocket on pedal}}{\text{Diameter of sprocket on rear wheel}}\times{\text{Circumference of rear wheel}}\\ =1.1\times \frac{6}{4}\times 26\pi\\ =134.77432\ inches/s$

Converting to mph

$1\ inch/s=\frac{1}{63360}\times 3600\ mph$

$134.77432\ inches/s=134.77432\times \frac{1}{63360}\times 3600\ mph=7.65763\ mph$

The Speed of the bicycle is 7.8 mph