document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346023>Question 346023</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 #247555 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247555\">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.<BR>\n" );
document.write( " If they are in the same direction, it will take the faster train 3 minutes to pass the slower one.<BR>\n" );
document.write( " If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains?<BR>\n" );
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document.write( "Let a = speed of the faster train<BR>\n" );
document.write( "let b = speed of the slower<BR>\n" );
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document.write( "Trains meeting each other<BR>\n" );
document.write( "The sum of the speed of the two trains (in meters/sec) <BR>\n" );
document.write( "speed = dist/time<BR>\n" );
document.write( "a + b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28130%2B120%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28%28130%2B120%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a + b = 20.83 m/sec is the sum of their speeds<BR>\n" );
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document.write( "Trains going in the same direction (change 3 min to 180 sec<BR>\n" );
document.write( "a - b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28130%2B120%29%29%2F180 ALIGN=MIDDLE  ALT=\"%28%28130%2B120%29%29%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a - b = 1.39 m/sec is the difference of their speed<BR>\n" );
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document.write( "Use elimination<BR>\n" );
document.write( "a + b = 20.83<BR>\n" );
document.write( "a - b = 1.39<BR>\n" );
document.write( "----------------adding eliminates b, find a<BR>\n" );
document.write( "2a = 22.22<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.22%2F2 ALIGN=MIDDLE  ALT=\"22.22%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 11.11 m/sec is the speed of train a<BR>\n" );
document.write( "In km/hr: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2811.11%2A3600%29%29%2F1000 ALIGN=MIDDLE  ALT=\"%28%2811.11%2A3600%29%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > ~ 40 km/hr<BR>\n" );
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document.write( "then using the sum equation find b<BR>\n" );
document.write( "11.11 + b = 20.83<BR>\n" );
document.write( "b = 20.83 - 11.11<BR>\n" );
document.write( "b = 9.72 m/sec is the speed of train b<BR>\n" );
document.write( "In km/hr <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289.72%2A3600%29%29%2F1000 ALIGN=MIDDLE  ALT=\"%28%289.72%2A3600%29%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > ~ 35 km/hr\r<BR>\n" );
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document.write( " </SPAN>\n" );
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