document.write( "Question 1107449: Jake and Mike are running from point A to point B. Jake runs at a rate of 5 mph the whole way. Mike runs half the distance at 6 mph, then runs the rest at 4 mph. Which one reaches point B first? Explain \n" ); document.write( "
Algebra.Com's Answer #722455 by ikleyn(52847)\"\" \"About 
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\n" ); document.write( "To make the solution highly visible, assume that the whole distance is  120 miles.\r
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\n" ); document.write( "\n" ); document.write( "Then Jake spends   \"120%2F5\" = 24 hours.\r
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\n" ); document.write( "\n" ); document.write( "Mike spends   \"60%2F6\" + \"60%2F4\" = 10 + 15 = 25 hours.\r
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\n" ); document.write( "\n" ); document.write( "Jake is faster.\r
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document.write( "    For the general case, if D is the distance, then Jake spends  \"D%2F5\"  hours.   (1)\r\n" );
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document.write( "    Mike spends  \"%28%28D%2F2%29%29%2F6\" + \"%28%28D%2F2%29%29%2F4\" = \"D%2F12+%2B+D%2F8\" = \"%288%2AD+%2B+12%2AD%29%2F48\" = \"%2820%2AD%29%2F96\" = \"D%2F%28%2896%2F20%29%29\"  hours.    (2)\r\n" );
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document.write( "    In (2),  the denominator   \"96%2F20\"   is LESS THAN 5,  so the fraction  (2)  is GREATER  than fraction (1),\r\n" );
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document.write( "    which means, again, that Mike is slower.\r\n" );
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