document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888128>Question 888128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distances between villages A and B is 60km. Can three backpackers who are at A get to B in three hours, if they have a motorbike which is able to carry up to two people at a constant speed of 50km/h, and each of the three backpackers can walk at a constant speed of 5km/h? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537111 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=537111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think the fastest way for all three to get from<BR>\n" );
document.write( "A to B is for 2 of them to go by motorbike<BR>\n" );
document.write( "while the other 1 is walking, then one of the<BR>\n" );
document.write( "two at B turns right around, picks up the walking<BR>\n" );
document.write( "backpacker, and takes him to B.<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in hrs for two to get from A to B<BR>\n" );
document.write( "on the motorbike<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+=+50%2At%5B1%5D+ ALIGN=MIDDLE  ALT=\"+60+=+50%2At%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=+t%5B1%5D+=+6%2F5+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+6%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "During this time, the third backpacker has walked<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++d%5B1%5D+=+5%2A%28+6%2F5+%29+ ALIGN=MIDDLE  ALT=\"++d%5B1%5D+=+5%2A%28+6%2F5+%29+\"   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+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "One of them from B turns around and heads toward<BR>\n" );
document.write( "the walker<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time in hrs for them to meet<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B2%5D+ ALIGN=MIDDLE  ALT=\"+d%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the distance the motorbike travels<BR>\n" );
document.write( "until them meet<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+60+-+6+%29+-+d%5B2%5D+=+54+-+d%5B2%5D+ ALIGN=MIDDLE  ALT=\"+%28+60+-+6+%29+-+d%5B2%5D+=+54+-+d%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance<BR>\n" );
document.write( "the walker travels in that time<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Equation for motorbike:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B2%5D+=+50t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+d%5B2%5D+=+50t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for walker:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+54+-+d%5B2%5D+=+5t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+54+-+d%5B2%5D+=+5t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+54+-+50t%5B2%5D+=+5t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+54+-+50t%5B2%5D+=+5t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+55t%5B2%5D+=+54+ ALIGN=MIDDLE  ALT=\"+55t%5B2%5D+=+54+\"   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%5B2%5D+=+54%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+54%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+54%2F55+ ALIGN=MIDDLE  ALT=\"+54%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs, the walker has traveled<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B3%5D+=+5%2A%28+54%2F55+%29+ ALIGN=MIDDLE  ALT=\"+d%5B3%5D+=+5%2A%28+54%2F55+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5B3%5D+=+54%2F11+ ALIGN=MIDDLE  ALT=\"+d%5B3%5D+=+54%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The distance left for both to go on the <BR>\n" );
document.write( "motorbike to B is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+-+6+-+54%2F11+=+54+-+54%2F11+ ALIGN=MIDDLE  ALT=\"+60+-+6+-+54%2F11+=+54+-+54%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+594%2F11+-+54%2F11+=+540%2F11+ ALIGN=MIDDLE  ALT=\"+594%2F11+-+54%2F11+=+540%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" > km<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+540%2F11+=+50%2At%5B3%5D+ ALIGN=MIDDLE  ALT=\"+540%2F11+=+50%2At%5B3%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B3%5D+=+540%2F550+ ALIGN=MIDDLE  ALT=\"+t%5B3%5D+=+540%2F550+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B3%5D+=+54%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B3%5D+=+54%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+6%2F5+%2B+54%2F55+%2B+54%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+6%2F5+%2B+54%2F55+%2B+54%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+66%2F55+%2B+108%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+66%2F55+%2B+108%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+174%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+174%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+3+%2B+9%2F55+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+3+%2B+9%2F55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "It looks like they can't get from A to B in under 3 hrs<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=+d%5B1%5D+%2B+54+-+d%5B2%5D+%2B+540%2F11+=+60+ ALIGN=MIDDLE  ALT=\"+d%5B1%5D+%2B+54+-+d%5B2%5D+%2B+540%2F11+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6+%2B+54%2F11+%2B+540%2F11+=+60+ ALIGN=MIDDLE  ALT=\"+6+%2B+54%2F11+%2B+540%2F11+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+66%2F11+%2B+594%2F11+=+60+ ALIGN=MIDDLE  ALT=\"+66%2F11+%2B+594%2F11+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+660%2F11+=+60+ ALIGN=MIDDLE  ALT=\"+660%2F11+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+60+=+60+ ALIGN=MIDDLE  ALT=\"+60+=+60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Hope I got it\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );