document.write( "Question 1118151: The difference in the average speeds of two train is 25km/h, the faster train takes 2 hours less to travel 150km than the slower train takes to travel 125km. Find the speeds of the two trains \n" ); document.write( "

Algebra.Com's Answer #733411 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "Let x be the average speed of the slower train, in kilometers per hour.\r\n" );
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document.write( "Then the speed of the faster train is (x+25) km/h.\r\n" );
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document.write( "The slower train takes   hours    to travel 125 kilometers.\r\n" );
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document.write( "The faster train takes   hours  to travel 150 kilometers.\r\n" );
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document.write( "The condition says that the faster train takes 2 hours less:\r\n" );
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document.write( " -  = 2   hours.     \r\n" );
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document.write( "It is yours \"time\" equation.     // As soon as I got this equation, I just know the answer: x = 25.  (I solved the equation in my head)\r\n" );
document.write( "                                 // But I will pretend that I don't know the solution, and will solve it formally (i.e. \"honestly\")\r\n" );
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document.write( "To solve it, multiply both sides by x*(x+25). You will get\r\n" );
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document.write( "125*(x+25) - 150*x = 2x*(x+25),\r\n" );
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document.write( "125x + 125*25 - 150x = 2x^2 + 50x,\r\n" );
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document.write( "2x^2 + 75x - 125*25 = 0,\r\n" );
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document.write( "2x^2 - 50x + 125x - 125*25 = 0,   <<<---=== starting from this line, I work to factor left side\r\n" );
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document.write( "2x*(x-25) + 125(x-25) = 0,\r\n" );
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document.write( "(2x+125)*(x-25) = 0.\r\n" );
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document.write( "The only positive root is  x= 25,  and it is the only solution to the problem.\r\n" );
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document.write( "Answer.  The slower train average speed is 25 km/h.  The faster train 25+25 = 50 km/h.\r\n" );
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document.write( "Check.    -  = 5 - 3 = 2.  ! The time equation is satisfied !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and checked.\r
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