document.write( "Question 36026: It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the rate of the freight train. Find the times and rates of both trains.
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Algebra.Com's Answer #22045 by stanbon(75887)\"\" \"About 
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It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the rate of the freight train. Find the times and rates of both trains.\r
\n" ); document.write( "\n" ); document.write( "Freight train Data:
\n" ); document.write( "distance=300 miles; time=x+2 hrs rate=300/(x+2) mph
\n" ); document.write( "Express train Data:
\n" ); document.write( "distance=280; time=x hrs; rate=280/x mph
\n" ); document.write( "EQUATION:
\n" ); document.write( "rate of express train = rate of freight train + 20\r
\n" ); document.write( "\n" ); document.write( "280/x = 300/(x+2) + 20\r
\n" ); document.write( "\n" ); document.write( "Multiply through by x(x+2)
\n" ); document.write( "280(x+2)=300x + 20x(x+2)
\n" ); document.write( "280x+560 = 300x+20x^2+40x
\n" ); document.write( "20x^2+60x-560=0
\n" ); document.write( "Divide thru by \"20\" to get:
\n" ); document.write( "x^2+3x-28=0
\n" ); document.write( "(x+7)(x-4)=0
\n" ); document.write( "x=4 hrs (time for the express train)
\n" ); document.write( "280/x=70mph (rate of the express train)
\n" ); document.write( "x+2=6 hrs (time for the freight train)
\n" ); document.write( "300/(x+2)=300/6=50 mph (rate of the freight train)
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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