precalc
posted by syd .
a 21speed bike has varying top speeds dependent on the gear it's in. the bike's tire diameter is 26 inches. the bike can pedal at a maximum of 130 revolutions per minute. the front chain wheel has sprokets of 24, 32, and 40 teeth. the rear cassette sprokets have 28, 24, 21, 18, 16, 14, 12 teeth. the bike's gears are labeled 121. gears 17 associated with the smallest front chain wheel's sproket. clearly communicate the top speed (in miles per hour) in each gear.

I will do one of the combinations for you
front: 40 teeth
back wheel: 12 teeth
(this will be the gear that can produce the highest speed)
for each turn of the front sprocket the back wheel will turn 40/12 or 10/3 or 3 1/3 times
each revolution of the back wheel covers
2(26)pi inches or 163.3628 inches
so at 130 rpm of the front sprocket, the back will will cover
130(10/3)163.3628 inches/minute
= 1.117275 miles/min (I divided by 5280*12)
~= 67 mph (I multiplied by 60)
you do the rest,
can you see the only part that would change ??? 
I think Reiny used the rire diameter for the radius, so the speed is two tiomes too high.
This question was posted and answered previously 
See your other post at http://www.jiskha.com/display.cgi?id=1232509956

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