document.write( "Question 1109352: Henry and Harriet are running around an oval that has a perimeter of 400m. Henry takes two and a half minutes to run a full lap while Harriet takes two minutes to run a full lap. If they both start at the same time and run in the same direction, how long will it take Harriet to lap Henry? \n" ); document.write( "
Algebra.Com's Answer #724342 by ikleyn(52832)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Let L be the \"oval perimeter\" length.\r
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document.write( "    The condition says that L = 400 meters.\r\n" );
document.write( "    But in reality, with all other given data, the solution below is VALID for any value of L: it DOES NOT DEPEND on the concrete value of L\r\n" );
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document.write( "     Henry'   speed is  \"L%2F2.5\"  units of L per minute.\r\n" );
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document.write( "     Harriet' speed is  \"L%2F2\" units of L per minute.\r\n" );
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document.write( "     The relative speed is  \"L%2F2+-+L%2F2.5\" = \"L%2A%281%2F2+-+1%2F2.5%29\" = \"2L%2A%28%281%2F4%29-%281%2F5%29%29\" = \"2L%2A%285%2F20-4%2F20%29\" = \"%282L%29%2A%281%2F20%29\" = \"L%2F10\" units of L per minute.\r\n" );
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document.write( "     It means that after start, the distance between Harriet (who runs faster) and Henry will increase at the rate of \"L%2F10\" per minute.\r\n" );
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document.write( "     Hence, Harriet will win one lap in 10 minutes.\r\n" );
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document.write( "     Notice that the solution does not depend on the concrete value of L.\r\n" );
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document.write( "     The distance along the oval from the starting point is\r\n" );
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document.write( "        D1 = \"%28L%2F2.5%29%2At\" for Henry   (=speed*time)\r\n" );
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document.write( "        D2 = \"%28L%2F2%29%2At\" for Harriet.\r\n" );
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document.write( "     The condition  D2 -D1 = L  is\r\n" );
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document.write( "        \"%28L%2F2%29%2At+-+%28L%2F2.5%29%2At\" = L,\r\n" );
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document.write( "        \"%28L%2F4+-+L%2F5%29%2A2t\" = L,\r\n" );
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document.write( "        \"%285L%29%2F20+-+%284L%29%2F20%29%2A2t\" = L,\r\n" );
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document.write( "        \"%28L%2F20%29%2A2t\" = L,\r\n" );
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document.write( "        \"%28L%2F10%29%2At\" = L\r\n" );
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document.write( "     and gives, finally, the same answer  t = \"L%2F%28%28L%2F10%29%29\" = 10 minutes.\r\n" );
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\n" ); document.write( "To see many other similar  (or closely related)  solved problems,  look into the lesson \r
\n" ); document.write( "\n" ); document.write( "    - Problems on bodies moving on a circle \r
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