You are riding a bicycle along a level road Assume each whee

You are riding a bicycle along a level road. Assume each wheel is 27 inches in diameter, the rear sprocket has a radius of 3 inches, and the front sprocket has a radius of 7 inches. How fast do you need to pedal (in revolutions per minute) to achieve a speed of 30 mph? (Round your answer to the nearest whole number.) rpm

Solution

let\'s start with the rear wheel
circumference / rev is the key to these problems
27\" diameter is a circumference / rev of 27pi

(30mi / hr) * (rev / 27pi \") * (12\" / ft)*(5280ft / mi) * (hr / 60 min) = 373.48 rpm for the rear wheel

the rear sprocket is also turning at 452.49 rpm, but at a radius of 3 \", or a circumference / rev of 6pi \"

(373.48 rev / min) * (6pi \" / rev) =
7040 \" / min, which is the linear speed of the chain-- same at the rear wheel and the front pedal sprocket (at a radius of 7\")

(7040\" / min )(rev / (14pi\")) = 160.06 rpm

so you need to pedal at 160.06 rpm on the 7\" ring to achieve a speed of 30 mph on the 27\" diameter rear wheel