document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675983>Question 675983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a 30 mile race between Joe and Frank, Joe started an hour after frank and finished an hour before Frank. Joe's average speed was 1 mile per hour faster than Franks. Find Joe and Frank's average seed during the race. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420152 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=420152\">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;\" > = Frank's speed in mi/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+1+ ALIGN=MIDDLE  ALT=\"+s+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Joe's speed in mi/hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%2A1+=+s+ ALIGN=MIDDLE  ALT=\"+s%2A1+=+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Frank's head start in miles<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Frank's time after his head start<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+-+1+ ALIGN=MIDDLE  ALT=\"+t+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Joe's time after Frank's head start<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Frank's equation:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+-+s++=+s%2At+ ALIGN=MIDDLE  ALT=\"+30+-+s++=+s%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Joe's equation:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+%28+s+%2B+1+%29%2A%28+t+-+1+%29+ ALIGN=MIDDLE  ALT=\"+30+=+%28+s+%2B+1+%29%2A%28+t+-+1+%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=+30+=+s%2At+%2B+t+-+s+-+1+ ALIGN=MIDDLE  ALT=\"+30+=+s%2At+%2B+t+-+s+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+t%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+30+=+t%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%29+\"   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=+t+=+%28+30+-+s+%29+%2F+s+ ALIGN=MIDDLE  ALT=\"+t+=+%28+30+-+s+%29+%2F+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+%281%2Fs%29%2A%28+30+-+s+%29%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+30+=+%281%2Fs%29%2A%28+30+-+s+%29%2A%28+s+%2B+1+%29+-+%28+s+%2B+1+%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=+30+=+%281%2Fs%29%2A%28+30s+-+s%5E2+%2B+30+-+s+%29+-+%28+s+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+30+=+%281%2Fs%29%2A%28+30s+-+s%5E2+%2B+30+-+s+%29+-+%28+s+%2B+1+%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=+30+=+30+-+s+%2B+30%2Fs+-+1+-+s+-+1+ ALIGN=MIDDLE  ALT=\"+30+=+30+-+s+%2B+30%2Fs+-+1+-+s+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30%2Fs+=+2s+%2B+2+ ALIGN=MIDDLE  ALT=\"+30%2Fs+=+2s+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+30+=+2s%5E2+%2B+2s+ ALIGN=MIDDLE  ALT=\"+30+=+2s%5E2+%2B+2s+\"   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+s+-+15+=+0+ ALIGN=MIDDLE  ALT=\"+s%5E2+%2B+s+-+15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<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+=+1+ ALIGN=MIDDLE  ALT=\"+b+=+1+\"   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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28-15%29+%29%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+s+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28-15%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+=+%28-1+%2B-+sqrt%28+1+%2B+60+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+s+=+%28-1+%2B-+sqrt%28+1+%2B+60+%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+%28-1+%2B+sqrt%28+61+%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+s+=+%28-1+%2B+sqrt%28+61+%29%29+%2F+2+\"   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+-1+%2B+7.8103+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+s+=+%28+-1+%2B+7.8103+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+6.8103%2F2+ ALIGN=MIDDLE  ALT=\"+s+=+6.8103%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+=+3.4051+ ALIGN=MIDDLE  ALT=\"+s+=+3.4051+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr = Frank's speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+%2B+1+=+4.4051+ ALIGN=MIDDLE  ALT=\"+s+%2B+1+=+4.4051+\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi/hr = Joe's speed<BR>\n" );
document.write( "My math could have got messed up- check it\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );