document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854011>Question 854011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help. I am having trouble setting up the equation.\r<BR>\n" );
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document.write( "A cyclist rides a distance of 100 miles to a distant city. His return trip takes 3 hours longer because his speed decreases by 30 mph. How fast did he ride each way?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514410 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=514410\">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=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his speed riding to the city<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s-30+ ALIGN=MIDDLE  ALT=\"+s-30+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his speed returning<BR>\n" );
document.write( "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;\" > = his time in hours to get to the city<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+%2B+3+ ALIGN=MIDDLE  ALT=\"+t+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = his time returning<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "Equation for 1st trip:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+s%2At+ ALIGN=MIDDLE  ALT=\"+100+=+s%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for return trip<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+%28+s+-+30+%29%2A%28+t+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+100+=+%28+s+-+30+%29%2A%28+t+%2B+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=+100+=+s%2At+-+30t+%2B+3s+-+90+ ALIGN=MIDDLE  ALT=\"+100+=+s%2At+-+30t+%2B+3s+-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+%28+t+%2B+3+%29%2As+-+30t+-+90+ ALIGN=MIDDLE  ALT=\"+100+=+%28+t+%2B+3+%29%2As+-+30t+-+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+t+%2B+3+%29%2As+=+30t+%2B+190+ ALIGN=MIDDLE  ALT=\"+%28+t+%2B+3+%29%2As+=+30t+%2B+190+\"   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+=+%28+30t+%2B+190+%29+%2F+%28+t+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+s+=+%28+30t+%2B+190+%29+%2F+%28+t+%2B+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this result into (1)<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+%28+t%2A%28+30t+%2B+190+%29%29+%2F+%28+t+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+100+=+%28+t%2A%28+30t+%2B+190+%29%29+%2F+%28+t+%2B+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100t+%2B+300+=+30t%5E2+%2B+190t+ ALIGN=MIDDLE  ALT=\"+100t+%2B+300+=+30t%5E2+%2B+190t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30t%5E2+%2B+90t+-+300+=+0+ ALIGN=MIDDLE  ALT=\"+30t%5E2+%2B+90t+-+300+=+0+\"   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%5E2+%2B+3t+-+10+=+0+ ALIGN=MIDDLE  ALT=\"+t%5E2+%2B+3t+-+10+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can see by looking at it, this is:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+t+%2B+5+%29%2A%28+t+-+2+%29+ ALIGN=MIDDLE  ALT=\"+%28+t+%2B+5+%29%2A%28+t+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2+ ALIGN=MIDDLE  ALT=\"+t+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( because time is positive, not negative )<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2+ ALIGN=MIDDLE  ALT=\"+t+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs is his time to get to the city<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+%2B+3+=+5+ ALIGN=MIDDLE  ALT=\"+t+%2B+3+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs is his time to return<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+s%2At+ ALIGN=MIDDLE  ALT=\"+100+=+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=+100+=+s%2A2+ ALIGN=MIDDLE  ALT=\"+100+=+s%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+50+ ALIGN=MIDDLE  ALT=\"+s+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100+=+%28+s+-+30+%29%2A%28+t+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+100+=+%28+s+-+30+%29%2A%28+t+%2B+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=+100+=+%28+s+-+30+%29%2A5+ ALIGN=MIDDLE  ALT=\"+100+=+%28+s+-+30+%29%2A5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+=+s+-+30+ ALIGN=MIDDLE  ALT=\"+20+=+s+-+30+\"   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+=+20+%2B+30+ ALIGN=MIDDLE  ALT=\"+s+=+20+%2B+30+\"   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+=+50+ ALIGN=MIDDLE  ALT=\"+s+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );