document.write( "Question 1138412: Inez can run at a rate that is 2 miles per hour faster
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Algebra.Com's Answer #756208 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " There are many ways to solve this problem.\r
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document.write( "Let x be Olivia's rate (in miles per hour).\r\n" );
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document.write( "Then the Inez's rate is (x+2) mph, according to the condition.\r\n" );
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document.write( "Then you can write this \"distance\" equations\r\n" );
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document.write( "    (25/60 + t)*x = 5,     (1)\r\n" );
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document.write( "     t*(x+2)      = 5      (2)\r\n" );
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document.write( "In these equations, \" t \" is the time after Inez' start to the catching moment;\r\n" );
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document.write( "the left  side of the equation (1) is the distance ran by Olivia, while \r\n" );
document.write( "the right side of the equation (2) is the distance ran by Inez from the starting point \r\n" );
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document.write( "to the catching up point, and equations state that each of these distances is 5 miles long.\r\n" );
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document.write( "So, this system of two non-linear equations is one possible setup for the problem.\r\n" );
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document.write( "Another possible setup is this equation\r\n" );
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document.write( "     -  = ,     (3)\r\n" );
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document.write( "saying that the difference of two traveled times,  Olivia's time    and  Inez's time  ,  is  25 minutes, \r\n" );
document.write( "or    of an hour.\r\n" );
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document.write( "This equation (3) is called the \"time\" equation.\r\n" );
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document.write( "I prefer this second setup and will show you on how to solve this equation (3).\r\n" );
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document.write( "Multiply both sides by  60x*(x+2)  to get\r\n" );
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document.write( "    300(x+2) - 300x = 25x*(x+2)\r\n" );
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document.write( "    300x + 600 - 300x = 25x^2 + 50x\r\n" );
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document.write( "    25x^2 + 50x - 600 = 0\r\n" );
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document.write( "    x^2 + 2x - 24 = 0\r\n" );
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document.write( "    (x+6)*(x-4) = 0\r\n" );
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document.write( "The roots are -6 and 4, and we accept only the positive value of 4 as the Olivia' speed.\r\n" );
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document.write( "ANSWER.  Olivia' speed is 4 mph;  Inez' speed is 4+2 = 6 mph.\r\n" );
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document.write( "CHECK.   Olivia's time is   hours = 1 hour and 15 minutes = 60 + 15 = 75 minutes.\r\n" );
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document.write( "         Inez's time is   hours = 50 minutes,\r\n" );
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document.write( "         and the difference is  75 minutes MINUS 50 minutes = 25 minutes,\r\n" );
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document.write( "         EXACTLY and PRECISELY as the problem states.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Using \"time\" equation is the STANDARD method of solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\r
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