document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936907>Question 936907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two trains pass each other in opposite directions. After 18 seconds the Locomotives are 500 m apart. If they travel at the same speeds in the same direction, they are 50 m apart after 15 seconds. Find the speeds of the two trains in km per hour. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #570373 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=570373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two trains pass each other in opposite directions.<BR>\n" );
document.write( " After 18 seconds the Locomotives are 500 m apart. <BR>\n" );
document.write( " If they travel at the same speeds in the same direction, they are 50 m apart after 15 seconds.<BR>\n" );
document.write( " Find the speeds of the two trains in km per hour.<BR>\n" );
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document.write( "let a = speed of one train (meters/sec)<BR>\n" );
document.write( "let b = speed of the other train<BR>\n" );
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document.write( "Write two distance equations, one for each way. dist = time * speed<BR>\n" );
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document.write( "18(a+b) = 500, going opposite directions, their speeds are additive<BR>\n" );
document.write( "15(a-b) = 50, going the same direction, their speed are subtracted<BR>\n" );
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document.write( "18a + 18b = 500<BR>\n" );
document.write( "15a - 15b = 50<BR>\n" );
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document.write( "multiply the first equation by 5, the 2nd equation by 6<BR>\n" );
document.write( "90a + 90b = 2500<BR>\n" );
document.write( "90a - 90b = 300<BR>\n" );
document.write( "------------------Adding eliminates b, find a<BR>\n" );
document.write( "180a = 2800<BR>\n" );
document.write( "a = 2800/180<BR>\n" );
document.write( "a = 15.555 m/sec<BR>\n" );
document.write( "Convert to km/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283600%2A15.5555%29%2F1000 ALIGN=MIDDLE  ALT=\"%283600%2A15.5555%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 56 km/hr, speed of train a<BR>\n" );
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document.write( "find b using the 1st equation<BR>\n" );
document.write( "18(15.555) + 18b = 500<BR>\n" );
document.write( "18b = 500 - 278<BR>\n" );
document.write( "18b = 220<BR>\n" );
document.write( "b = 220/18<BR>\n" );
document.write( "b = 12.222 m/sec<BR>\n" );
document.write( "convert to km/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283600%2A12.222%29%2F1000 ALIGN=MIDDLE  ALT=\"%283600%2A12.222%29%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 44 km/hr, speed of train b<BR>\n" );
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document.write( ";<BR>\n" );
document.write( "Confirm this using these values (m/sec) in the 2nd equation<BR>\n" );
document.write( "15(15.555) - 15(12.222) =<BR>\n" );
document.write( "233.3 - 183.3 = 50 m <BR>\n" );
document.write( " </SPAN>\n" );
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