document.write( "Question 1057376: max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in the same direction as max but at 96 km/h. assuming neither driver stops for a break, how far from kansas city will they be when olivia catches up with max? \n" ); document.write( "

Algebra.Com's Answer #672445 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in
\n" ); document.write( "the same direction as max but at 96 km/h. assuming neither driver stops for a break, how far from kansas city will
\n" ); document.write( "they be when olivia catches up with max?
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\n" ); document.write( "\n" ); document.write( "Solution 1\r
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document.write( " =  = 5 hours.     (*)\r\n" );
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document.write( "In 5 hours after Olivia's start she will catch up Max.\r\n" );
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document.write( "Olivia will travel 5*96 = 480 km.\r\n" );
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document.write( "Answer.  Olivia will catch up Max at 480 km from Kansas city.\r\n" );
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document.write( "Explanations.  In the formula (*) the numerator \"80\" is the distance between them when Olivia started her move.\r\n" );
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document.write( "               The denominator 96-80 = 16 km/h is their relative speed.\r\n" );
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document.write( "               The distance between them is decreased 16 km per hour, each hour.\r\n" );
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document.write( "               This \"16\" is the rate decreasing the distance between the two.\r\n" );
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document.write( "Let \"t\" be the time (in hours) after Olivia's start moment till the moment she will catches up Max. \r\n" );
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document.write( "Then the distance she will cover is 96*t.\r\n" );
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document.write( "Max will spent (t+1) hours and will cover the distance 80*(t+1).\r\n" );
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document.write( "These two distances are the same, so you get an equation \r\n" );
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document.write( "80*(t+1) = 96*t.\r\n" );
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document.write( "Simplify and solve for t:\r\n" );
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document.write( "80t + 80 = 96t,\r\n" );
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document.write( "80 = 96t - 80t,\r\n" );
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document.write( "16t = 80,\r\n" );
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document.write( "t =    (Do you recognize the formula (*) ?)\r\n" );
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document.write( "t = 5.\r\n" );
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document.write( "Thus Olivia will catch up Max in 5 hours and will cover the distance 5*96 = 480 kilometers.\r\n" );
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document.write( "The same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the introductory lesson on Travel and Distance problems\r
\n" ); document.write( "\n" ); document.write( " - Travel and Distance problems \r
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