# math

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The figure shown the chain drive of a bicycle. How far will the bicycle move if the pedals are rotated at 180°. Assume the radius of the bicycle wheel is 13.6 inches. There's a small circle w/a radius of 1.38 in and a large circle w/ 4.33 in.

• math -

assuming the pedal sprocket has a radius of 4.33 in
and the back wheel sprocket has the radius of 1.38 in

diameter of pedal wheel = 2π(4.33) = 27.20619
diameter of back wheel sprocket = 2π(1.38) = 8.670796

diameter of back wheel = 2π(13.6) = 85.45132

for each rotation of the pedal sprocket, the back wheel will rotate 27.20619/8.670796 times
= 3.13768 times

so it cover a distance of 3.13768 x 85.45132
= 268.119 inches.

or using a simple ratio ....
x/(2π(13.6)) = 2π(4.33)/(2π(1.38))
x = 2π(13.6)(4.33)/1.38

but that is the distance covered for one complete rotation of the pedals
We want 180° or 1/2 a rotation, so the distance covered is

134.06 inches or 11 feet 2 inches

• correction -math -

Where I said "diameter" I meant circumference

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