# Math

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If you are riding a bike and your front sprocket (the one with the pedals) has 40 teeth and the rear sprocket (the one connected to your back tire) has 20 teeth, and you are pedaling at a rate of 50 rpm, how fast are you going if your bike has 27 inch diameter wheels?

• Math -

Assuming the teeth are equally spaced, the circumference of the front sprocket is twice that of the real sprocket, or
for each turn of the front we have two turns of the rear
Then at 50 rpm, the rear will will turn 100 rpm

circumf of rear wheel = 27π inches
distance covered in 1 minute (from rpm=rotations per minute)

27π(100) inches
or 2700π inches per minute
= 706.858.. ft/min
= appr 8.03 mph

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