document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625091>Question 625091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Karnataka Express leaves Bangalore at 5 p.m. and reaches Dharmavaram at 9 p.m. Kurla Express leaves Dharmavaram at 7 p.m. and reaches Bangalore at 10.30 p.m. What time do the trains cross one another? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393302 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=393302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance between the cities<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of the Karnataka Express<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of the Kurla express<BR>\n" );
document.write( "How much of a head start does the Karnataka Express have?<BR>\n" );
document.write( "from 5 PM to 7 PM<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5Bh%5D+=+r%5B1%5D%2A2+ ALIGN=MIDDLE  ALT=\"+d%5Bh%5D+=+r%5B1%5D%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( any units for d[h] )<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+d%2F4+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+d%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+=+d%2F3.5+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+=+d%2F3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( any units for d - same as d[h] )<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Start a stopwatch when the Kurla Express leaves. They will both<BR>\n" );
document.write( "travel for the same 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;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Think of one train as standing still, and the other approaching<BR>\n" );
document.write( "at the sum of their speeds. The moving train must cover <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+-+2r%5B1%5D++=+d+-+2%2A%28d%2F4%29+ ALIGN=MIDDLE  ALT=\"+d+-+2r%5B1%5D++=+d+-+2%2A%28d%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of their speeds is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%2F4+%2B+d%2F3.5+ ALIGN=MIDDLE  ALT=\"+d%2F4+%2B+d%2F3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2At+ ALIGN=MIDDLE  ALT=\"+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%2F2+=+d%2A%28+1%2F4+%2B+1%2F3.5+%29%2At+ ALIGN=MIDDLE  ALT=\"+d%2F2+=+d%2A%28+1%2F4+%2B+1%2F3.5+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+=+%28+1%2F4+%2B+2%2F7+%29%2At+ ALIGN=MIDDLE  ALT=\"+1%2F2+=+%28+1%2F4+%2B+2%2F7+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+28+ ALIGN=MIDDLE  ALT=\"+28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14+=+%28+7+%2B+8+%29%2At+ ALIGN=MIDDLE  ALT=\"+14+=+%28+7+%2B+8+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+14%2F15+ ALIGN=MIDDLE  ALT=\"+t+=+14%2F15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+14%2F15%2A60+=+56+ ALIGN=MIDDLE  ALT=\"+14%2F15%2A60+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes<BR>\n" );
document.write( "They will meet at 56 minutes past 7<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2A%2814%2F15%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2A%2814%2F15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15%2F2+=+14%2F4+%2B+14%2F3.5+ ALIGN=MIDDLE  ALT=\"+15%2F2+=+14%2F4+%2B+14%2F3.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15%2F2+=+7%2F2+%2B+8%2F2+ ALIGN=MIDDLE  ALT=\"+15%2F2+=+7%2F2+%2B+8%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15%2F2+=+15%2F2+ ALIGN=MIDDLE  ALT=\"+15%2F2+=+15%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );