document.write( "Question 1184012: Two cars start out at the same spot. One car starts to drive north at 40 mph and 3 hours later the second car starts driving to the east at 60 mph. How long after the first car starts driving does it take for the two cars to be 500 miles apart? \n" ); document.write( "

Algebra.Com's Answer #814543 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Two cars start out at the same spot. One car starts to drive north at 40 mph.
\n" ); document.write( "3 hours later the second car starts driving to the east at 60 mph.
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document.write( "Let \"t\" be the time chronometered after the first car starts.\r\n" );
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document.write( "First car traveled t hours;  second car traveled  (t-3) hours  (assuming t >= 3).\r\n" );
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document.write( "The distance between the cars is then\r\n" );
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document.write( "     = 500.\r\n" );
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document.write( "It is the equation to solve in order for to find \"t\".\r\n" );
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document.write( "Square both side\r\n" );
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document.write( "    (40*t)^2 + (60*(t-3))^2 = 500^2\r\n" );
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document.write( "    1600t^2 + 3600t^2 - 3600*6t + 9*3600 = 250000\r\n" );
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document.write( "    5200t^2 - 21600t + 32400 = 250000\r\n" );
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document.write( "    5200t^2 - 21600t - 217600 = 0.\r\n" );
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document.write( "    520t^2  - 2160t  - 21760 = 0\r\n" );
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document.write( "Use the quadratic formula.  The positive root is approximately 8.87 hours.\r\n" );
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document.write( "ANSWER.  8.87 hours after the first car started.\r\n" );
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document.write( "CHECK.   = 500 miles (total distance).   ! Correct !\r\n" );
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