https://artofproblemsolving.com/wiki/index.php?title=1952_AHSME_Problems/Problem_10&feed=atom&action=history
1952 AHSME Problems/Problem 10 - Revision history
2024-03-29T07:31:39Z
Revision history for this page on the wiki
MediaWiki 1.31.1
https://artofproblemsolving.com/wiki/index.php?title=1952_AHSME_Problems/Problem_10&diff=71231&oldid=prev
1=2: Added categories: Introductory Algebra Problems, Rate Problems
2015-07-18T21:11:00Z
<p>Added categories: Introductory Algebra Problems, Rate Problems</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 21:11, 18 July 2015</td>
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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>==See also==</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>==See also==</div></td></tr>
<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>{{AHSME 50p box|year=1952|num-b=9|num-a=11}}</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>{{AHSME 50p box|year=1952|num-b=9|num-a=11}}</div></td></tr>
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1=2
https://artofproblemsolving.com/wiki/index.php?title=1952_AHSME_Problems/Problem_10&diff=58524&oldid=prev
Throwaway1489: Created page with "== Problem== An automobile went up a hill at a speed of <math> 10 </math> miles an hour and down the same distance at a speed of <math> 20 </math> miles an hour. The average spe..."
2014-01-02T21:34:46Z
<p>Created page with "== Problem== An automobile went up a hill at a speed of <math> 10 </math> miles an hour and down the same distance at a speed of <math> 20 </math> miles an hour. The average spe..."</p>
<p><b>New page</b></p><div>== Problem==<br />
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An automobile went up a hill at a speed of <math> 10 </math> miles an hour and down the same distance at a speed of <math> 20 </math> miles an hour. The average speed for the round trip was:<br />
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<math> \textbf{(A) \ }12\frac{1}{2}\text{mph} \qquad \textbf{(B) \ }13\frac{1}{3}\text{mph} \qquad \textbf{(C) \ }14\frac{1}{2}\text{mph} \qquad \textbf{(D) \ }15\text{mph} \qquad \textbf{(E) \ }\text{none of these} </math><br />
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==Solution==<br />
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Let <math> r </math>, <math> t </math>, and <math> d </math> represent the rate, time, and distance (respectively) of each trip. We know that <math> rt=d </math>, or <math> r_1t_1=r_2t_2 </math>. Because it is given that <math> 2r_1=r_2 </math>, <math> t_1=2t_2 </math>. Furthermore, <math> d=10t_1=20t_2 </math>. The average speed can be expressed as <math> \frac{2d}{t_1+t_2}=\frac{2(20t_2)}{2t_2+t_2}=\frac{40}{3}=\boxed{\textbf{(B)}\ 13\frac{1}{3}\text{ mph}} </math>.<br />
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==See also==<br />
{{AHSME 50p box|year=1952|num-b=9|num-a=11}}<br />
{{MAA Notice}}</div>
Throwaway1489