document.write( "Question 389044: a and b are two station 300 km apert.Two train start simultaneously from a and b, each to the opposite station .The train from a reaches b 9 hours , the train from b reaches a 4 hours after they meet, Find the rate at which each train travels? slove the problem.
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Algebra.Com's Answer #275555 by jrfrunner(365)\"\" \"About 
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The trains meet somewhere between station a and station b
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\n" ); document.write( "let train 1 \"from\" station a
\n" ); document.write( "let train 2 \"from\" station b
\n" ); document.write( "let d1=distance train 1 travels after meeting train 2
\n" ); document.write( "let d2=distance train 2 travels after meeting train 1
\n" ); document.write( "let r1=rate of train 1
\n" ); document.write( "let r2=rate of train 2
\n" ); document.write( "let t=time when trains meet
\n" ); document.write( "distance =rate * time or d=r*t
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\n" ); document.write( "from meeting point to station a: train 1 has travelled r1*t
\n" ); document.write( "and train 2 will travel 4 hours to get to station a or r2*4
\n" ); document.write( "so... r1*t = r2*4
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\n" ); document.write( "likewise
\n" ); document.write( "r2*t=r1*9
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\n" ); document.write( "solving for t: r2*4/r1=t and r1*9/r2=t
\n" ); document.write( "4*r2/r1=9*r1/r2
\n" ); document.write( "4r2^2=9*r1^2 (cross multiply)
\n" ); document.write( "2*r2=3*r1
\n" ); document.write( "2*r2/3=r1
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\n" ); document.write( "we also know that the total distance is 300, so
\n" ); document.write( "d1+d2=300
\n" ); document.write( "4*r2+9*r1=300
\n" ); document.write( "4*r2+9*(2*r2/3)=300
\n" ); document.write( "4*r2+6r*2=300
\n" ); document.write( "10*r2=300
\n" ); document.write( "r2=30
\n" ); document.write( "r1=2*r2/3=20\r
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