Posted by **syd** on Tuesday, January 20, 2009 at 10:41pm.

a 21-speed 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 1-21. gears 1-7 associated with the smallest front chain wheel's sproket. clearly communicate the top speed (in miles per hour) in each gear.

- precalc -
**Reiny**, Tuesday, January 20, 2009 at 11:04pm
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 ???

- precalc -
**drwls**, Wednesday, January 21, 2009 at 10:41am
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

- precalc -
**drwls**, Wednesday, January 21, 2009 at 10:44am
See your other post at http://www.jiskha.com/display.cgi?id=1232509956

- zubdce jlek -
**zubdce jlek**, Tuesday, February 10, 2009 at 5:50pm
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