document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634130>Question 634130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help please ,\r<BR>\n" );
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document.write( "Two trains travel round toy railway track, one takes 40 secs per circuit, the other takes 55 secs.\r<BR>\n" );
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document.write( "How long before they are back in the station together?\r<BR>\n" );
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document.write( "Look forward to a reply\r<BR>\n" );
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document.write( "Best regards and many thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399390 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=399390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the length of the track isn't given,<BR>\n" );
document.write( "I'll say it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+ ALIGN=MIDDLE  ALT=\"+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units.<BR>\n" );
document.write( "So the faster train's speed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+%2F+40+=+1+ ALIGN=MIDDLE  ALT=\"+40+%2F+40+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit/sec<BR>\n" );
document.write( "The slower train's speed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40%2F55+ ALIGN=MIDDLE  ALT=\"+40%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units/sec<BR>\n" );
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document.write( "I think of the round track as straightened out <BR>\n" );
document.write( "with a mark on the track every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+ ALIGN=MIDDLE  ALT=\"+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units.<BR>\n" );
document.write( "Then the problem becomes:<BR>\n" );
document.write( "\"What is the smallest time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when they both <BR>\n" );
document.write( "end up on a mark?\" The mark is really the same point<BR>\n" );
document.write( "repeated.<BR>\n" );
document.write( "The faster train:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+j%2A40+=+1%2At+ ALIGN=MIDDLE  ALT=\"+j%2A40+=+1%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slower train:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%2A40+=+%2840%2F55%29%2At+ ALIGN=MIDDLE  ALT=\"+k%2A40+=+%2840%2F55%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( j and k are whole numbers )<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Solving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+40j+ ALIGN=MIDDLE  ALT=\"+t+=+40j+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+55k+ ALIGN=MIDDLE  ALT=\"+t+=+55k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40j+=+55k+ ALIGN=MIDDLE  ALT=\"+40j+=+55k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+j%2Fk+=+55%2F40+ ALIGN=MIDDLE  ALT=\"+j%2Fk+=+55%2F40+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+j%2Fk+=+11%2F8+ ALIGN=MIDDLE  ALT=\"+j%2Fk+=+11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------<BR>\n" );
document.write( "This tells me the faster train goes around 11 times,<BR>\n" );
document.write( "and the slower train goes around 8 times in time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , meeting back at the start<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+40j+ ALIGN=MIDDLE  ALT=\"+t+=+40j+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+40%2A11+ ALIGN=MIDDLE  ALT=\"+t+=+40%2A11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+440+ ALIGN=MIDDLE  ALT=\"+t+=+440+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "and, checking<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+55k+ ALIGN=MIDDLE  ALT=\"+t+=+55k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+55%2A8+ ALIGN=MIDDLE  ALT=\"+t+=+55%2A8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+440+ ALIGN=MIDDLE  ALT=\"+t+=+440+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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