document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922500>Question 922500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Erica noted that a train to Muizenberg took 8 minutes to pass her. A train in the opposite direction to Cape Town took 12 minutes to pass her. The trains took 9 minutes to pass each other. Assuming each tram mamtained a constant speed, and given that the train to Cape Town was 150m long, what was the length of the train to Muizenberg? (15) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559619 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=559619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Erica noted that a train to Muizenberg took 8 minutes to pass her.<BR>\n" );
document.write( " A train in the opposite direction to Cape Town took 12 minutes to pass her.<BR>\n" );
document.write( " The trains took 9 minutes to pass each other.<BR>\n" );
document.write( " Assuming each tram maintained a constant speed, and given that the train to Cape Town was 150m long, what was the length of the train to Muizenberg?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Are you sure that the time intervals you give here are minutes and not seconds?<BR>\n" );
document.write( "If the C.T. train was 150 m long took 12 min to pass a point, that is not even 1 km/h<BR>\n" );
document.write( "However, if it took 12 sec: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F12 ALIGN=MIDDLE  ALT=\"150%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3600%2F1000 ALIGN=MIDDLE  ALT=\"3600%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 45 km/h, a reasonable speed.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let m = speed of the Muiz train in m/sec<BR>\n" );
document.write( "Let L = length of the Muiz train in meters<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the speed of the C.T train<BR>\n" );
document.write( "150/12 = 12.5 m/sec<BR>\n" );
document.write( "and likewise the Muiz train<BR>\n" );
document.write( "m = L/8<BR>\n" );
document.write( "Or<BR>\n" );
document.write( "L = 8m<BR>\n" );
document.write( ":<BR>\n" );
document.write( "When the trains go toward each other, the relative speed = m + 12.5<BR>\n" );
document.write( "The lengths of both trains is added together: L + 150<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L+%2B+150%29%2F%28m%2B12.5%29 ALIGN=MIDDLE  ALT=\"%28L+%2B+150%29%2F%28m%2B12.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9 sec <BR>\n" );
document.write( "replace L with 8m<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288m+%2B+150%29%2F%28m%2B12.5%29 ALIGN=MIDDLE  ALT=\"%288m+%2B+150%29%2F%28m%2B12.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9 sec<BR>\n" );
document.write( "therefore <BR>\n" );
document.write( "8m + 150 = 9(m+12.5)<BR>\n" );
document.write( "8m + 150 = 9m + 112.5<BR>\n" );
document.write( "150 - 112.5 = 9m - 8m<BR>\n" );
document.write( "m = 37.5 m/sec the speed of the Muiz train<BR>\n" );
document.write( "Find the length of the train<BR>\n" );
document.write( "8(37.5) = 300 meters length of the Muiz train </SPAN>\n" );
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