Question

You travel again in your trusty car with the 25 inch wheels. You installed a nifty gadget that measures how often your wheels turn each hour. It shows that right now they turn 54000 times per hour. You figure you are going at a speed of miles per hour. (Round your answer to the nearest tenth of a mile per hour.) Hint: Multiply the circumference of the wheel with the number of rotations per hour. Convert inches to miles.

Answer 1

hmmm so the wheel has a diameter of 25", that means it has a radius of half that or 12.5", let's find out its circumference or arc

`\textit{Circumference of a Circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.5 \end{cases}\implies C=2\pi (12.5)\implies C=25\pi ~inches`

now we know the wheel is turning 54000 times per hour and since each time is 25π inches, that's (25π)(54000) inches total. We know there are 12" in one foot and 5280 feet in 1 mile, so

`(25\pi )(54000)~in*\cfrac{feet}{12~in}*\cfrac{miles}{5280~feet}\implies \cfrac{(25\pi )(54000)}{(12)(5280)}miles \\\\\\ \cfrac{1875\pi }{88}miles ~~ \approx ~~ \text{\LARGE 66.9}~\textit{miles per hour}`