document.write( "Question 1182960: Justin recently drove to visit his parents who live 504 miles away. On his way there his average speed was 16 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 16 hours driving, find the two rates. \n" ); document.write( "

Algebra.Com's Answer #813082 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Justin recently drove to visit his parents who live 504 miles away.
\n" ); document.write( "On his way there his average speed was 16 miles per hour faster than on his way home (he ran into some bad weather).
\n" ); document.write( "If Justin spent a total of 16 hours driving, find the two rates.
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document.write( "Let x be the slower rate, in miles per hour.\r\n" );
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document.write( "Then the faster rate is  (x+16) mph.\r\n" );
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document.write( "The time traveling \"there\" is    hours.\r\n" );
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document.write( "The time traveling  back   is         hours.\r\n" );
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document.write( "The total time is 16 hours, giving you the \"time\" equation\r\n" );
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document.write( "     +  = 16  hours.\r\n" );
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document.write( "To solve this equation, multiply both sides by x*(x+16) and simplify\r\n" );
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document.write( "    504x + 504(x+16) = 16x*(x+16)\r\n" );
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document.write( "     63x + 63(x+16) = 2x*(x+16)\r\n" );
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document.write( "     63x + 63x + 63*16 = 2x^2 + 32x\r\n" );
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document.write( "      2x^2 - 94x - 1008 = 0\r\n" );
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document.write( "       x^2 - 47x - 504 = 0\r\n" );
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document.write( "You can solve it by using the quadratic formula or by factoring\r\n" );
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document.write( "      (x-56)*(x+9) = 0\r\n" );
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document.write( "Since you need the positive root, only, you choose  x = 56.\r\n" );
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document.write( "ANSWER.  The rate traveling back is 56 mph;  the rate traveling to \"there\" was 56+16 = 72 mph.\r\n" );
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document.write( "CHECK.   +  = 7 + 9 = 16  hours.   ! correct !\r\n" );
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