document.write( "Question 1195276: Two railway stations are at a distance of 96 km from each other. One train covers this distance in 40 minutes less than the other. The speed of the first train is 12 km/h faster than that of the second. Determine the speeds of both the trains. \n" ); document.write( "

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Two railway stations are at a distance of 96 km from each other. One train covers this distance in 40 minutes less than the other. The speed of the first train is 12 km/h faster than that of the second. Determine the speeds of both the trains.
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\n" ); document.write( "For the slower train, t = d/r = 96/r
\n" ); document.write( "For the faster, t- 2/3 = 96/(r+12)
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\n" ); document.write( "96/r - 2/3 = 96/(r+12)
\n" ); document.write( "Multiply by 3r
\n" ); document.write( "288 - 2r = 96*3r/(r+12)
\n" ); document.write( "144 - r = 144r/(r+12)
\n" ); document.write( "(144-r)*(r+12) = 144r
\n" ); document.write( "-r^2 + 132r + 1728 = 144r
\n" ); document.write( "-r^2 - 12r + 1728 = 0
\n" ); document.write( "r^2 + 12r - 1728 = 0
\n" ); document.write( "(r+48)*(r-36) = 0
\n" ); document.write( "---------------
\n" ); document.write( "Slow train goes 36 km/hr
\n" ); document.write( "Fast train goes 48 km/hr
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