## Bicycle Tire

A $26$-inch (diameter) bicycle tire is being calibrated with a speedometer. Approximately how many revolutions of the wheel are equal to $1$ mile?
Source: NCTM Math Teacher 2008

SOLUTION
Circumference of tire
$2\pi r=\pi d$ where $d$ is the diameter.
Length of $1$ revolution = $26\pi$ in.
Let $x$ be the number of revolutions in $1$ mile.
$x\times 26\pi in\times\dfrac{1 ft}{12 in}\times\dfrac{1 mile}{5280 ft}=1 mile$
$x=\dfrac{12\times 5280}{26\pi}=775.7$

Answer: $775.7$ revolutions