document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=775842>Question 775842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes 12 seconds for two trains to pass one another when moving in opposite directions. If they are in the same direction, it will take the faster train 3 minutes to pass the slower one. If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473203 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It takes 12 seconds for two trains to pass one another when moving in opposite directions. If they are in the same direction, it will take the faster train 3 minutes to pass the slower one. If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains?\r<BR>\n" );
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document.write( "train I speed = x<BR>\n" );
document.write( "train II speed =y\r<BR>\n" );
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document.write( "When they are in opposite direction the effective speed = x+y\r<BR>\n" );
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document.write( "Time taken = 12 seconds = 12/3600  hrs. = 1/300 hours\r<BR>\n" );
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document.write( "The total length of trains is the distance d=250 m = 0.25 km\r<BR>\n" );
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document.write( "Distance = speed * time\r<BR>\n" );
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document.write( "(x+y)*1/300 =0. 250\r<BR>\n" );
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document.write( "When in same direction\r<BR>\n" );
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document.write( "effective speed = x-y<BR>\n" );
document.write( "time = 3 minutes = 3/60 = 1/20 hours\r<BR>\n" );
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document.write( "(x-y)*1/20 = 0.250\r<BR>\n" );
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document.write( "(x+y)*1/300 = 0.250\r<BR>\n" );
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document.write( "x+y = 75<BR>\n" );
document.write( "x-y= 5\r<BR>\n" );
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document.write( "Add the two equations\r<BR>\n" );
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document.write( "2x=80\r<BR>\n" );
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document.write( "x=40 => speed of Train I\r<BR>\n" );
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document.write( "x+y=75\r<BR>\n" );
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document.write( "so speed of Train II = 75-40=35 kph\r<BR>\n" );
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document.write( " </SPAN>\n" );
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