document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059912>Question 1059912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a bicyclist is traveling 41 miles at a certain speed, the return speed is made 6 mph slower. The total time for the round trip is 15 hours. What is the average speed of the bicyclist on the first trip?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674961 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=674961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=speed<BR>\n" );
document.write( "x*t=distance<BR>\n" );
document.write( "x*t=41, so the outbound time is 41/x<BR>\n" );
document.write( "(x-6)*t=41<BR>\n" );
document.write( "t=41/(x-6), which is the inbound time.<BR>\n" );
document.write( "Both times add to 15<BR>\n" );
document.write( "41/x+{41/(x-6)}=15<BR>\n" );
document.write( "Clear fractions by multiplying everything by x(x-6)<BR>\n" );
document.write( "41(x-6)+41x=15x(x-6)<BR>\n" );
document.write( "41x-246+41x=15x^2-90x<BR>\n" );
document.write( "15x^2-172x+246=0<BR>\n" );
document.write( "x=(1/30)(172+/-sqrt (172^2-60*246); sqrt 14824=121.75<BR>\n" );
document.write( "x=(1/30)(293.75)=9.79 mph<BR>\n" );
document.write( "x=(1/30)(50.25)=1.675 mph, and that can't work because x-6 would be negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C15%2C-300%2C300%2C15x%5E2-172x%2B246%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C15%2C-300%2C300%2C15x%5E2-172x%2B246%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At 9.79 mph, it takes 4.19 hours outbound  ANSWER 9.79 mph<BR>\n" );
document.write( "At 3.79 mph, it takes 10.82 hours inbound<BR>\n" );
document.write( "They add to 15.01, or 15 with rounding error. </SPAN>\n" );
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