Algebra.Com's Answer #835534 by ikleyn(52776)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Hello I'm having trouble setting this problem up. Any help would be appreciated. Thanks.
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document.write( "A traveler having 18 miles to go, calculates that his usual rate would make
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document.write( "him one-half hour late for an appointment; he finds that in order to arrive on
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document.write( "time he must travel at a rate one-half mile an hour faster. What is his usual rate?
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document.write( "Let x be his usual rate, in miles per hour.\r\n" );
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document.write( "The time to travel 18 miles at his usual rate is  hours.\r\n" );
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document.write( "The time to travel with the faster rate, (x+0.5) miles per hour, is  hours.\r\n" );
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document.write( "The longer time is  of an hour longer:\r\n" );
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document.write( " - = of an hour. (1)\r\n" );
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document.write( " | At this point, the setup is complete: |\r\n" );
document.write( " | you just have an equation to solve. |\r\n" );
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document.write( "To solve it, multiply both sides by 2x*(x+0.5) = 2x^2 + x. You will get\r\n" );
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document.write( " 36(x+0.5) - 36x = x^2 + 0.5x\r\n" );
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document.write( " 36x + 18 - 36x = x^2 + 0.5x\r\n" );
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document.write( " x^2 + 0.5x - 18 = 0\r\n" );
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document.write( "  =  =  =  .\r\n" );
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document.write( "Obviously, only positive root fits x =  =  = 4 miles per hour.\r\n" );
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document.write( "Check it, by substituting into equation (1)\r\n" );
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document.write( "  = 4.5 - 4 = 0.5 = of an hour. ! correct !\r\n" );
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document.write( "ANSWER. The usual rate is 4 miles per hour.\r\n" );
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document.write( "Solved.\r
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