Algebra.Com's Answer #847540 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Mike can run the mile in 6 minutes, and Dan can run the mile in 9 minutes.
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document.write( "If Mike gives Dan a head start of 1 minute,
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document.write( "(a) how far from the start will Mike pass Dan?
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document.write( "(b) How long does it take?
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document.write( "So, in this problem, Dan starts first and runs with the speed  of a mile per minute.\r\n" );
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document.write( " Mike starts one minute after Dan and runs with the speed  of a mile per minute.\r\n" );
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document.write( "Let t be the time after Dan starts.\r\n" );
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document.write( "The distance formula for Dan is D(t) =  miles.\r\n" );
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document.write( "The distance formula for Mike is M(t) =  miles.\r\n" );
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document.write( "Mike passes Dan when the distances are the same\r\n" );
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document.write( " = ,\r\n" );
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document.write( "or, cross-multiplying\r\n" );
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document.write( " 6t = 9(t-1) ---> 6t = 9t - 9 ---> 9 = 9t - 6t ---> 9 = 3t ---> t = 9/3 = 3 minutes.\r\n" );
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document.write( "So, Mike passes Dan in 3 minutes after Dan starts, or in 2 minutes after Mike starts. <<<---=== ANSWER to (b)\r\n" );
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document.write( "Mike will pass Dan at the distance =  miles =  miles from the start. <<<---=== ANSWER to (a)\r\n" );
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document.write( "Solved.\r
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