document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=232410>Question 232410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three motorists A, B and C often travel on a certain highway, and each motorist always travels at a constant speed. A is the fastest of the three and C the slowest. \r<BR>\n" );
document.write( "\n" );
document.write( "One day, when the three travel in the same direction, B overtakes C, five minutes later, A overtakes C and in another 3 minutes, A overtakes B. On another occasion when they again travel in the same direction, A overtakes B first, then, nine minutes later, A overtakes C. When will B overtake C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171765 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=171765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I tried to extract the information that<BR>\n" );
document.write( "would lead to a solution.<BR>\n" );
document.write( "(a) In both trips, B is the only one that starts and finishes<BR>\n" );
document.write( "(b) Nothing is known about speeds or distances, only times<BR>\n" );
document.write( "(c) For the 1st trip, C travels for 5 min, then A travels for 3 min<BR>\n" );
document.write( "(d) For the 2nd trip, A travels for 9 min, then C travels for ? min<BR>\n" );
document.write( "--------------------------------------------------------------------<BR>\n" );
document.write( "I set up this ratio:<BR>\n" );
document.write( "(A's time on 1st trip) / (time for 1st trip which is B's time) = <BR>\n" );
document.write( "(A's time on 2nd trip) / (time for 2nd trip which is B's time)<BR>\n" );
document.write( "And I could have used this ratio, too:<BR>\n" );
document.write( "(C's time on 1st trip) / (time for 1st trip which is B's time) = <BR>\n" );
document.write( "(C's time on 2nd trip) / (time for 2nd trip which is B's time)<BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > = C's time for last part of 2nd trip (B overtakes C) <BR>\n" );
document.write( "Using the 1st ratio:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8+=+9%2F%289+%2B+C%29 ALIGN=MIDDLE  ALT=\"3%2F8+=+9%2F%289+%2B+C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%289+%2B+C%29+=+72 ALIGN=MIDDLE  ALT=\"3%2A%289+%2B+C%29+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+%2B+3C+=+72 ALIGN=MIDDLE  ALT=\"27+%2B+3C+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C+=+45 ALIGN=MIDDLE  ALT=\"3C+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+15 ALIGN=MIDDLE  ALT=\"C+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Using the 2nd ratio:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8+=+C%2F%289+%2B+C%29 ALIGN=MIDDLE  ALT=\"5%2F8+=+C%2F%289+%2B+C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8C+=+5%2A%289%2BC%29 ALIGN=MIDDLE  ALT=\"8C+=+5%2A%289%2BC%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8C+=+45+%2B+5C ALIGN=MIDDLE  ALT=\"8C+=+45+%2B+5C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C+=+45 ALIGN=MIDDLE  ALT=\"3C+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+15 ALIGN=MIDDLE  ALT=\"C+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "B will overtake C in 15 min<BR>\n" );
document.write( "and<BR>\n" );
document.write( "Plugging <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+15 ALIGN=MIDDLE  ALT=\"C+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into the ratios, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8+=+9%2F24 ALIGN=MIDDLE  ALT=\"3%2F8+=+9%2F24\"   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=5%2F8+=+15%2F24 ALIGN=MIDDLE  ALT=\"5%2F8+=+15%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both are true\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );