Question

The diameter of each wheel of a bicycle is 27 in. If you are traveling at a speed of 40 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning

Answer 1

Circumference = πd, where d = diameter

we know the wheel has a diameter of 27 inches, so the total circumference is 27π, and that's the arc length of one revolution.

there are 5280 feet in 1 mile and 12 inches in 1 foot.

so in 40 miles there are 40(5280)(12) inches.

and we also know that there are 60 minutes in 1 hour.

$\cfrac{40~miles}{hour}\implies \cfrac{~~ \frac{40(5280)(12)~in}{27\pi ~\frac{in}{rev}}~~}{60~minutes}~~\approx ~~\cfrac{29878.688~rev}{60~minutes}~~ \approx ~~497.978~\frac{rev}{minute}$