document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=728481>Question 728481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To travel 84 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 42 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #445468 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=445468\">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=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Doreen's time in hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+3+ ALIGN=MIDDLE  ALT=\"+t+-+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Sue's time in hrs ,   <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Doreen's speed in mi/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+15+ ALIGN=MIDDLE  ALT=\"+s+%2B+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Sue's speed in mi/hr<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Doreen's equation:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+s%2At+ ALIGN=MIDDLE  ALT=\"+42+=+s%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sue's equation:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+ ALIGN=MIDDLE  ALT=\"+84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+s%2At+%2B+15t+-+3s+-+45+ ALIGN=MIDDLE  ALT=\"+84+=+s%2At+%2B+15t+-+3s+-+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+42%2Fs+ ALIGN=MIDDLE  ALT=\"+t+=+42%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=+84+=+s%2A%2842%2Fs%29+%2B+15%2A%2842%2Fs%29+-+3s+-+45+ ALIGN=MIDDLE  ALT=\"+84+=+s%2A%2842%2Fs%29+%2B+15%2A%2842%2Fs%29+-+3s+-+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+42+%2B+630%2Fs+-+3s+-45+ ALIGN=MIDDLE  ALT=\"+84+=+42+%2B+630%2Fs+-+3s+-45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+87+=+630%2Fs+-+3s+ ALIGN=MIDDLE  ALT=\"+87+=+630%2Fs+-+3s+\"   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=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+87s+=+630+-+3s%5E2+ ALIGN=MIDDLE  ALT=\"+87s+=+630+-+3s%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3s%5E2+%2B+87s+-+630+=+0+ ALIGN=MIDDLE  ALT=\"+3s%5E2+%2B+87s+-+630+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5E2+%2B+29s+-+210+=+0+ ALIGN=MIDDLE  ALT=\"+s%5E2+%2B+29s+-+210+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1 ALIGN=MIDDLE  ALT=\"+a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+29+ ALIGN=MIDDLE  ALT=\"+b+=+29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-210+ ALIGN=MIDDLE  ALT=\"+c+=+-210+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-29+%2B-+sqrt%28+29%5E2+-+4%2A1%2A%28-210%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+s+=+%28-29+%2B-+sqrt%28+29%5E2+-+4%2A1%2A%28-210%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-29+%2B-+sqrt%28+841+%2B+840%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+s+=+%28-29+%2B-+sqrt%28+841+%2B+840%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-29+%2B-+sqrt%28+1681%29%29%2F2+ ALIGN=MIDDLE  ALT=\"+s+=+%28-29+%2B-+sqrt%28+1681%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-29+%2B+41%29%2F2+ ALIGN=MIDDLE  ALT=\"+s+=+%28-29+%2B+41%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( ignore negative sqrt- can't have negative speed )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+12%2F2+ ALIGN=MIDDLE  ALT=\"+s+=+12%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+6+ ALIGN=MIDDLE  ALT=\"+s+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+15+=+21+ ALIGN=MIDDLE  ALT=\"+s+%2B+15+=+21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+42%2Fs+ ALIGN=MIDDLE  ALT=\"+t+=+42%2Fs+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+42%2F6+ ALIGN=MIDDLE  ALT=\"+t+=+42%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+7+ ALIGN=MIDDLE  ALT=\"+t+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+3+=+4+ ALIGN=MIDDLE  ALT=\"+t+-+3+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Sue's time: 4 hrs<BR>\n" );
document.write( "Doreen's time: 7 hrs<BR>\n" );
document.write( "Sue's speed: 21 mi/hr<BR>\n" );
document.write( "Doreen's speed: 6 mi/hr<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+ ALIGN=MIDDLE  ALT=\"+84+=+%28+s+%2B+15+%29%2A%28+t+-+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+%28+6+%2B+15+%29%2A%28+7+-+3+%29+ ALIGN=MIDDLE  ALT=\"+84+=+%28+6+%2B+15+%29%2A%28+7+-+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+21%2A4+ ALIGN=MIDDLE  ALT=\"+84+=+21%2A4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+84+=+84+ ALIGN=MIDDLE  ALT=\"+84+=+84+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+s%2At+ ALIGN=MIDDLE  ALT=\"+42+=+s%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=+42+=+6%2A7+ ALIGN=MIDDLE  ALT=\"+42+=+6%2A7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+42+=+42+ ALIGN=MIDDLE  ALT=\"+42+=+42+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );