+33 A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. The cyclist pedals at 190 rpm
Find the linear speed of the bicycle in in/min (correct to at least two decimal places)
How fast is the bike moving in mph (to two decimal places)?
+129657 Because the chain moves at the same speed over both sprockets......the rear sprocket must make 7/4 revolutions for every one revolution made by the front sprocket
So.....when the rider moves the front sprocket through 190 revs/min......the rear sprocket moves through 190 (7/4) = 332.5 revs/min......and the back wheel will rotate at the same rate
So....the linear speed of the bicycle in inches per minute =
2pi * 9 * 332.5 = about 18802.43 in/min
The speed in mph =
[2pi *9 * 332.5]inches per minute * 60 minutes in 1 hr / [63360 in/ mile] = about 17.27 mph
