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Difference between revisions of "1953 AHSME Problems/Problem 10"

(Created page with "== Problem == The number of revolutions of a wheel, with fixed center and with an outside diameter of <math>6</math> feet, required to cause a point on the rim to go one mile...")
(No difference)

Revision as of 15:32, 23 June 2016

Problem

The number of revolutions of a wheel, with fixed center and with an outside diameter of $6$ feet, required to cause a point on the rim to go one mile is:

$\textbf{(A)}\ 880 \qquad\textbf{(B)}\ \frac{440}{\pi} \qquad\textbf{(C)}\ \frac{880}{\pi} \qquad\textbf{(D)}\ 440\pi\qquad\textbf{(E)}\ \text{none of these}$

Solution

We know that the radius of the wheel is $3$ feet, so the total circumference of the wheel is $6\pi$ feet. We also know that one mile is equivalent to $5280$ feet. It takes $\frac{5280}{6\pi}$ revolutions for any one point on the wheel to travel a mile. Simplifying, we find that the answer is $\boxed{\textbf{(C) } \frac{880}{\pi}}$.

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