document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262931>Question 262931</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? \r<BR>\n" );
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document.write( "A. 2 hours <BR>\n" );
document.write( "B. 4 ½ hours <BR>\n" );
document.write( "C. 5 ¾ hours <BR>\n" );
document.write( "D. 6 hours <BR>\n" );
document.write( "E. 7 ½ hours \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193806 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=193806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a stopwatch and I'll start it when the 2nd <BR>\n" );
document.write( "cyclist leaves. At that time the 1st cyclist has gone<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D%2A3 ALIGN=MIDDLE  ALT=\"r%5B1%5D%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A3+=+18 ALIGN=MIDDLE  ALT=\"6%2A3+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "Now they will each go for the same time on my stopwatch, so<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;\" >, which I'll just call <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( "<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( "<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( "From these,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D%2Fr%5B1%5D+=+d%5B2%5D%2Fr%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D%2Fr%5B1%5D+=+d%5B2%5D%2Fr%5B2%5D\"   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%2Ar%5B2%5D+=+d%5B2%5D%2Ar%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D%2Ar%5B2%5D+=+d%5B2%5D%2Ar%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%5B1%5D+=+6d%5B2%5D ALIGN=MIDDLE  ALT=\"10d%5B1%5D+=+6d%5B2%5D\"   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+=+.6d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+.6d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I know 1 more thing about the distances:<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;\" >, since the 2nd cyclist has to make up <BR>\n" );
document.write( "the headstart the 1st one got<BR>\n" );
document.write( "Substituting:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+.6d%5B2%5D+%2B+18 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+.6d%5B2%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=.4d%5B2%5D+=+18 ALIGN=MIDDLE  ALT=\".4d%5B2%5D+=+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%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+=+.6%2Ad%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+.6%2Ad%5B2%5D\"   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+=+.6%2A45 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+.6%2A45\"   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+=+27 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "Now, I need to find <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=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( "(2) <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( "-------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+=+6t ALIGN=MIDDLE  ALT=\"27+=+6t\"   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( "and, also<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+=+10t ALIGN=MIDDLE  ALT=\"45+=+10t\"   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( "How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? <BR>\n" );
document.write( "This means that the 3 hr headstart is not to be included in answer<BR>\n" );
document.write( "so, 4.5 hrs will pass <BR>\n" );
document.write( "The answer is B\r<BR>\n" );
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