Question

A bicycle with tires of radius r=15 inches is being ridden by a boy at a constant speed - the tires are making five rotations per second. How many miles will he ride in minutes? (1mi = 5280 ft)

Algebra foundations
A bicycle with tires of radius r=15 inches is being ridden by a boy at a constant speed - the tires are making five rotations per second. How many miles will he ride in minutes? (1mi = 5280 ft)

2021-01-20
First, we find the speed in ft/s:
$$\displaystyle{v}=ω×{r}$$
$$\displaystyle{v}={\left({\left({5}{r}{o}{t}{a}{t}{i}{o}{n}\frac{{s}}{{\sec}}\right)}\cdot{\left({2}π{r}{a}{d}{i}{a}{n}\frac{{s}}{{1}}{r}{o}{t}{a}{t}{i}{o}{n}\right)}\right)}{\left({15}\in\cdot{\left({1}{f}\frac{{t}}{{12}}\in.\right)}\right.}$$
$$\displaystyle{v}={12.5}π{f}\frac{{t}}{{s}}$$
15 minutes = 900 seconds so the distance traveled is:
$$\displaystyle{d}={\left({12.5}π{f}\frac{{t}}{{s}}\right)}{\left({900}{s}\right)}$$
$$\displaystyle{d}={11250}π{f}\frac{{t}}{{s}}$$
In miles,
$$\displaystyle{d}={11250}π{f}{t}\cdot{\left({1}{m}\frac{{i}}{{5280}}{f}{t}\right)}≈{6.7}{m}{i}\le{s}$$