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	<title>Comments on: FR. Who Wants To Be A Mathematician?</title>
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		<title>By: strauss</title>
		<link>http://mathfactor.uark.edu/2009/04/fr-who-wants-to-be-a-mathematician/comment-page-1/#comment-504</link>
		<dc:creator>strauss</dc:creator>
		<pubDate>Fri, 01 May 2009 15:32:39 +0000</pubDate>
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		<description>
Stephen S writes:

Firstly, Hi, found your show and have listened to all the back podcasts now to catch up. Yes I have quite a long drive some days. I&#039;m in Bath in the UK by the way.

Secondly, the quick car trip question is false, since I can do the whole trip at 60 miles an hour 50 miles, fiftt mins) and never do 50 at all. In fact I could do 49 miles in 1 min and take the last 1 at a very lesuirely pace to do the time and distance.

Actually, in the real world, I&#039;d allow 35 mins to do 50 miles as this is Europe - assuming a clear road and sleeping cops. (Which around here is often...)


We note:

Glad we&#039;ve made your drives go by quicker!

Let&#039;s see, even if you drove 49 miles in one minute (at a steady rate of 49 miles per minute) and then covered the rest in 49 minutes at (at a steady rate of 1/49 miles per minute) there&#039;d still be the ten minute interval from 0:48 through 10:48 in which you&#039;d drive exactly 10 miles!

(That is, you&#039;d drive 1/5 of a minute at 49 mpm, and 49/5 minutes at 1/49 mpm, for a grand total of 10 miles)

So this would still work out!

Thanks for writing, and thanks for listening!

Chaim


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		<content:encoded><![CDATA[<p>Stephen S writes:</p>
<p>Firstly, Hi, found your show and have listened to all the back podcasts now to catch up. Yes I have quite a long drive some days. I&#8217;m in Bath in the UK by the way.</p>
<p>Secondly, the quick car trip question is false, since I can do the whole trip at 60 miles an hour 50 miles, fiftt mins) and never do 50 at all. In fact I could do 49 miles in 1 min and take the last 1 at a very lesuirely pace to do the time and distance.</p>
<p>Actually, in the real world, I&#8217;d allow 35 mins to do 50 miles as this is Europe &#8211; assuming a clear road and sleeping cops. (Which around here is often&#8230;)</p>
<p>We note:</p>
<p>Glad we&#8217;ve made your drives go by quicker!</p>
<p>Let&#8217;s see, even if you drove 49 miles in one minute (at a steady rate of 49 miles per minute) and then covered the rest in 49 minutes at (at a steady rate of 1/49 miles per minute) there&#8217;d still be the ten minute interval from 0:48 through 10:48 in which you&#8217;d drive exactly 10 miles!</p>
<p>(That is, you&#8217;d drive 1/5 of a minute at 49 mpm, and 49/5 minutes at 1/49 mpm, for a grand total of 10 miles)</p>
<p>So this would still work out!</p>
<p>Thanks for writing, and thanks for listening!</p>
<p>Chaim</p>
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		<title>By: pgc</title>
		<link>http://mathfactor.uark.edu/2009/04/fr-who-wants-to-be-a-mathematician/comment-page-1/#comment-503</link>
		<dc:creator>pgc</dc:creator>
		<pubDate>Fri, 01 May 2009 13:55:15 +0000</pubDate>
		<guid isPermaLink="false">http://mathfactor.uark.edu/?p=567#comment-503</guid>
		<description>[spoiler]
Suppose that we cover 50 miles in 50 minutes but that there is no 10 minute period that covers 10 miles.

If the fist 10 minutes covers less than 10 miles, then every 10 minute period must cover less than 10 miles (since otherwise we&#039;d have to pass through an occasion where we covered exactly 10 miles in 10 minutes). It follows that we must travel less than 50 miles in the full 50 minutes.

Similarly if the first 10 minutes cover more than 10 miles then the overall trip would cover more than 50 miles in 50 minutes since we&#039;d never be allowed to slow down enough without violating the initial supposition.

So that&#039;s a proof by contradiction that for there must be a 10 minute period that covers exactly 10 miles.
[/spoiler]</description>
		<content:encoded><![CDATA[<p><a href="javascript:void(null);" onclick="s_toggleDisplay(document.getElementById('SID2062082407'), this, 'Show Spoiler &#9660;', 'Hide Spoiler &#9650;');">Show Spoiler &#9660;</a></p>
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<p>Suppose that we cover 50 miles in 50 minutes but that there is no 10 minute period that covers 10 miles.</p>
<p>If the fist 10 minutes covers less than 10 miles, then every 10 minute period must cover less than 10 miles (since otherwise we&#8217;d have to pass through an occasion where we covered exactly 10 miles in 10 minutes). It follows that we must travel less than 50 miles in the full 50 minutes.</p>
<p>Similarly if the first 10 minutes cover more than 10 miles then the overall trip would cover more than 50 miles in 50 minutes since we&#8217;d never be allowed to slow down enough without violating the initial supposition.</p>
<p>So that&#8217;s a proof by contradiction that for there must be a 10 minute period that covers exactly 10 miles.</p>
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