document.write( "Question 426400: It takes a freight train 3 hours more to travel 280 miles than it takes an express train to travel 200 miles. The rate of the express is 10 miles per hour faster the the rate of the freight train. Fine the rates of both trains. \n" ); document.write( "

Algebra.Com's Answer #853204 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "It takes a freight train 3 hours more to travel 280 miles than it takes an express train to travel 200 miles.
\n" ); document.write( "The rate of the express is 10 miles per hour faster the rate of the freight train. Fine the rates of both trains.
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect - it has fatal arithmetical errors.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
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document.write( "Freight train speed  x     mph, distance 280 miles, travel time is   hours.\r\n" );
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document.write( "Express train speed (x+10) mph, distance 200 miles, travel time is   hours.\r\n" );
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document.write( "Time equation\r\n" );
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document.write( "     =  + 3.    (1)\r\n" );
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document.write( "Multiply all the terms by x(x+10)\r\n" );
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document.write( "    280(x+10) = 200x + 3x*(x+10).\r\n" );
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document.write( "Reduce to the standard form quadratic equation\r\n" );
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document.write( "    280x + 2800 = 200x + 3x^2 + 30x\r\n" );
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document.write( "    3x^2 - 50x - 2800 = 0.\r\n" );
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document.write( "Use the quadratic formula and find the roots.\r\n" );
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document.write( "To avoid mechanical calculations, I used the online solver\r\n" );
document.write( "https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php/\r\n" );
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document.write( "It produced two roots - one was positive, the other was negative.\r\n" );
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document.write( "I rejected the negative root and accepted the positive one, which was 40.\r\n" );
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document.write( "So, the freight train speed was 40 mph, while the express train speed w3as 40+10 = 50 mph.   <<<---===  ANSWER\r\n" );
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document.write( "CHECK  equation (1).\r\n" );
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document.write( "       Its left side is   = 7.\r\n" );
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document.write( "       Its right side is   + 3 = 7.\r\n" );
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document.write( "       Both values coincide - hence, the solution is correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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