Algebra.Com's Answer #847502 by ikleyn(52803)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The Gare Montparnasse train station in Paris has a high-speed version of a moving walkway.
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document.write( "If he walks while riding this moving walkway, Jean Claude can travel 200 meters in 30 seconds
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document.write( "less time than if he stands still on the moving walkway. If Jean Claude walks at a normal rate
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document.write( "of 1.5 meters per second, what is the speed of the Gare Montparnasse walkway?
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document.write( "Let x be the speed of the walkway, in meters per second.\r\n" );
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document.write( "When Jean Claude stands still on the walkway, he actually moves relatively to the floor\r\n" );
document.write( "at the speed of x m/second.\r\n" );
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document.write( "The time to travel 200 meters at this speed is  seconds.\r\n" );
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document.write( "When Jean Claude walks on the walkway with his relative speed of 1.5 m/s relative to the walkway,\r\n" );
document.write( "he actually moves relatively to the floor at the speed of (1.5+x) m/second.\r\n" );
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document.write( "The time to travel 200 meters at this speed is  seconds.\r\n" );
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document.write( "The difference of the two travel times is 30 seconds - so, we write this time equation\r\n" );
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document.write( " - = 30 seconds. (1)\r\n" );
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document.write( "This is your setup equation.\r\n" );
document.write( "At this point, the setup is complete, and now your task is to solve it.\r\n" );
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document.write( "To solve the equation, multiply both sides by x*(x+1.5). You will get\r\n" );
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document.write( " 200*(x+1.5) - 200*x = 30x*(x+1.5).\r\n" );
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document.write( "Simplify step by step\r\n" );
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document.write( " 200x + 300 - 200x = 30x^2 + 45x,\r\n" );
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document.write( " 300 = 30x^2 + 45x,\r\n" );
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document.write( "divide all the terms by 15\r\n" );
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document.write( " 20 = 2x^2 + 3x,\r\n" );
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document.write( " 2x^2 + 3x - 20 = 0.\r\n" );
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document.write( "Apply the quadratic formula\r\n" );
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document.write( "  =  =  =  .\r\n" );
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document.write( "You want the positive root x =  =  = 2.5 m/s.\r\n" );
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document.write( "It is the speed of the walkway. ANSWER\r\n" );
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document.write( "CHECK. Check the validity of equation (1):  -  = -  = 30.0 seconds.\r\n" );
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document.write( " Which is precisely correct !\r\n" );
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document.write( "At this point, the problem is solved completely.\r
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