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 #296641 by mananth(16946) $\"\"$ $\"About$

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Freight train x mph 280 miles
\n" ); document.write( "Express train x +10 mph 200 miles
\n" ); document.write( "
\n" ); document.write( "t=d/r
\n" ); document.write( "280/x=200/(x+10)+3
\n" ); document.write( "280/x-200 /(x+10)=3
\n" ); document.write( "LCD = x(x+10)
\n" ); document.write( "Multiply by LCD
\n" ); document.write( "280(x+10)-200x=3x(x+10)
\n" ); document.write( "280x+2800-200*x =3x^2+30
\n" ); document.write( "3X^2+80x-2770=0
\n" ); document.write( "Find the roots of the equation by quadratic formula
\n" ); document.write( "a=3 b=80 c=-2770
\n" ); document.write( "b^2-4ac=6400+33240
\n" ); document.write( "b^2-4ac=39640
\n" ); document.write( " $\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( " $\"x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"$
\n" ); document.write( "x1=(-80 +199.1)/6
\n" ); document.write( "x1=19.85
\n" ); document.write( "x2=(-80 -199.1)/6
\n" ); document.write( "x2= -46.52
\n" ); document.write( "Ignore negative value
\n" ); document.write( "x=19.85 mph Freight train speed
\n" ); document.write( "29.85 mph=Express train speed
\n" ); document.write( " \n" ); document.write( "

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