https://artofproblemsolving.com/wiki/index.php?title=1953_AHSME_Problems/Problem_10&feed=atom&action=history1953 AHSME Problems/Problem 10 - Revision history2024-03-28T08:36:25ZRevision history for this page on the wikiMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=1953_AHSME_Problems/Problem_10&diff=85123&oldid=prevXiej at 00:47, 2 April 20172017-04-02T00:47:37Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We know that the radius of the wheel is <math>3</math> feet, so the total circumference of the wheel is <math>6\pi</math> feet. We also know that one mile is equivalent to <math>5280</math> feet. It takes <math>\frac{5280}{6\pi}</math> revolutions for any one point on the wheel to travel a mile. Simplifying, we find that the answer is <math>\boxed{\textbf{(C) } \frac{880}{\pi}}</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We know that the radius of the wheel is <math>3</math> feet, so the total circumference of the wheel is <math>6\pi</math> feet. We also know that one mile is equivalent to <math>5280</math> feet. It takes <math>\frac{5280}{6\pi}</math> revolutions for any one point on the wheel to travel a mile. Simplifying, we find that the answer is <math>\boxed{\textbf{(C) } \frac{880}{\pi}}</math>.</div></td></tr>
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</table>Xiejhttps://artofproblemsolving.com/wiki/index.php?title=1953_AHSME_Problems/Problem_10&diff=79039&oldid=prevHiabc: 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..."2016-06-23T19:32:44Z<p>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..."</p>
<p><b>New page</b></p><div>== Problem ==<br />
<br />
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 is: <br />
<br />
<math>\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}</math><br />
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== Solution ==<br />
<br />
We know that the radius of the wheel is <math>3</math> feet, so the total circumference of the wheel is <math>6\pi</math> feet. We also know that one mile is equivalent to <math>5280</math> feet. It takes <math>\frac{5280}{6\pi}</math> revolutions for any one point on the wheel to travel a mile. Simplifying, we find that the answer is <math>\boxed{\textbf{(C) } \frac{880}{\pi}}</math>.</div>Hiabc