if a bicycle has 26 inch diameter wheels, the front chain drive has a radius of 2.2 inches, and the back drive has a radius of 3 inches. how far does the bicycle travel every one rotation of the cranks (pedals)?

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- Feb 11th 2008, 08:14 PM08gakawatrigonometry word problem
if a bicycle has 26 inch diameter wheels, the front chain drive has a radius of 2.2 inches, and the back drive has a radius of 3 inches. how far does the bicycle travel every one rotation of the cranks (pedals)?

- Feb 11th 2008, 08:31 PMangel.white
The circumference is times diameter. So one rotation of the pedals will cause the front chain drive to complete one full turn, so it will move the chain the same distance as it's circumference. So it will move the chain inches. Then the back drive has a circumference of inches, but it only turns inches. So it turns of a full rotation. Since the wheel turns at the same rate as the back chain drive, the wheel will turn of a full turn as well. And since the back wheel is 26 inches in diameter, it's circumference is inches. If it turned a full rotation, it would go this distance along the ground, but it is only giong of this distance, so it is going inches. Or approximately 59.8997 inches.

...unless I misunderstood. - Feb 11th 2008, 08:45 PMearboth
- Feb 11th 2008, 09:08 PMangel.white
Good call, I didn't catch the switch from diameter on the wheel to radius on the gear.

so then:

Front gear:

Rear gear:

Ratio of turn on rear gear

Rear wheel turns the same portion of a full turn as the rear gear

A full turn would be it's circumference

(because it is given in diameter rather than radius as the gears are)

Ratio of a full turn

inches

Well, I ended up with the same answer because the 2's ended up canceling out in the ratio. Is this what you came up with earboth? I don't have much confidence in my answer. - Feb 19th 2008, 11:30 AMMontedorotypo in answer?
The answer given, 58.8997 should be 59.8997

Also, the response from earboth sez:

"When calculating the proportions the factor 2 cancels out so that your final result is correct."

The word "proportions" here should be the word "ratio".

Picky, indeed.

Greetings,

Montedoro - Feb 19th 2008, 05:48 PMangel.white