document.write( "Question 718412: A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go? \n" ); document.write( "

Algebra.Com's Answer #440893 by Edwin McCravy(20056) $\"\"$ $\"About$

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A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go?

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document.write( "That other \"tutor\" is only showing his ignorance of algebra.\r\n" );
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document.write( "Make this chart:\r\n" );
document.write( "                     Distance    Rate   Time\r\n" );
document.write( "Trip that happened      120        x     t     \r\n" );
document.write( "Trip that didn't        120      x+10   t-2\r\n" );
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document.write( "Use DISTANCE = RATE × TIME, we get this system\r\n" );
document.write( "from the chart:\r\n" );
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document.write( "         120 = xt\r\n" );
document.write( "         120 = (x+10)(t-2)\r\n" );
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document.write( "Since they're both equal to 120, set them equal\r\n" );
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document.write( "          xt = (x+10)(t-2)\r\n" );
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document.write( "Multiply out the right side\r\n" );
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document.write( "          xt = xt-2x+10t-20\r\n" );
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document.write( "Subtract xt from both sides:\r\n" );
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document.write( "           0 = -2x+10t-20\r\n" );
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document.write( "          2x = 10t-20\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "           x = 5t-10\r\n" );
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document.write( "Substitute 5t-10 for x in\r\n" );
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document.write( "         120 = xt\r\n" );
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document.write( "         120 = (5t-10)t\r\n" );
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document.write( "         120 = 5t²-10t\r\n" );
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document.write( "-5t²+10t+120 = 0\r\n" );
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document.write( "Divide through by -5\r\n" );
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document.write( "    t²-2t-24 = 0\r\n" );
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document.write( "  (t-6)(t+4) = 0\r\n" );
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document.write( "t-6 = 0;   t+4 = 0\r\n" );
document.write( "  t = 6;     t = -4 (ignore)\r\n" );
document.write( "  x = 5t-10\r\n" );
document.write( "  x = 5(6)-10\r\n" );
document.write( "  x = 30-10\r\n" );
document.write( "  x = 20\r\n" );
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document.write( "The train went 20 mph\r\n" );
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document.write( "Edwin

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