document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273582>Question 273582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2 CYCLIST START BIKING FROM A TRAIL START 3 HOURS APART. THE 2ND TRAVELS AT 10 MILES PER HOUR AND STARTS 3 HOURS AFTER THE 1ST WHO IS TRAVELING AT 6 MILES PER HOUR, HOW  MUCH TIME WILL PASS BEFORE SECOND CATCHEDS FIRST </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199822 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=199822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each cyclist must have their own <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=r%2At ALIGN=MIDDLE  ALT=\"d=r%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > equation<BR>\n" );
document.write( "1st cyclist:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5D%2At%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd cyclist:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5D%2At%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "The 1st cyclist has a head start which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr x <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+6 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+10 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Assume I have a stopwatch and I start it when<BR>\n" );
document.write( "the 2nd cyclist leaves. When I stop the watch<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > so I'll call them both <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( "The 2nd cyclist has to make up the head start, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+d%5B1%5D+%2B+18 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+d%5B1%5D+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5D%2At ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+6t ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+6t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5D%2At ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+%2B+18+=+10t ALIGN=MIDDLE  ALT=\"d%5B1%5D+%2B+18+=+10t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll substitute (1) into (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6t+%2B+18+=+10t ALIGN=MIDDLE  ALT=\"6t+%2B+18+=+10t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4t+=+18 ALIGN=MIDDLE  ALT=\"4t+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4.5 ALIGN=MIDDLE  ALT=\"t+=+4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "This is the elapsed time after the 1st cyclist got <BR>\n" );
document.write( "a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr head start, so<BR>\n" );
document.write( "the 2nd cyclist catches the 1st cyclist <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5+%2B+3+=+7.5 ALIGN=MIDDLE  ALT=\"4.5+%2B+3+=+7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "after the 1st cyclist left<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+10t ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+10t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+10%2A4.5 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+10%2A4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+45 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+6t+ ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+6t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+d%5B1%5D+%2B+18 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+d%5B1%5D+%2B+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+d%5B2%5D+-+18 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+d%5B2%5D+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+-+18+=+6%2A4.5 ALIGN=MIDDLE  ALT=\"d%5B2%5D+-+18+=+6%2A4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+-+18+=+27 ALIGN=MIDDLE  ALT=\"d%5B2%5D+-+18+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+45 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );