document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101908>Question 1101908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Members of the healthy running club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned along the same course, running at 10 km/h from the second rest stop to the first,and at 6 km/h the rest of the way to the club house. If it took a total of 2.5 h to run both ways between the club house and the first rest stop, and 3 hours to run both ways between the first and second rest stops, how far, in km, did they run altogether? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716616 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Members of the healthy running club ran from their club house to a first rest stop at a speed of 9 km/h, and from there to the second rest stop at a speed of 5 km/h. They returned along the same course, running at 10 km/h from the second rest stop to the first,and at 6 km/h the rest of the way to the club house. If it took a total of 2.5 h to run both ways between the club house and the first rest stop, and 3 hours to run both ways between the first and second rest stops, how far, in km, did they run altogether?<BR>\n" );
document.write( "ch->1rs->2rs<BR>\n" );
document.write( "9a+5x<BR>\n" );
document.write( "2rs->1rs->ch<BR>\n" );
document.write( "10y+6b\r<BR>\n" );
document.write( "\n" );
document.write( "x+y=3<BR>\n" );
document.write( "a+b=2.5<BR>\n" );
document.write( "9a+5x=10y+6b 1st to +2nd to =2nd fro+1st fro<BR>\n" );
document.write( "9a=6b \r<BR>\n" );
document.write( "\n" );
document.write( "a=6b/9<BR>\n" );
document.write( "a=2b/3<BR>\n" );
document.write( "a+b=2.5<BR>\n" );
document.write( "2b/3+b=2.5<BR>\n" );
document.write( "2b+3b=7.5<BR>\n" );
document.write( "5b=7.5<BR>\n" );
document.write( "b=7.5/5<BR>\n" );
document.write( "b=1.5<BR>\n" );
document.write( "a+b=2.5<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "5x=10y<BR>\n" );
document.write( "x=2y<BR>\n" );
document.write( "x+y=3<BR>\n" );
document.write( "2y+y=3<BR>\n" );
document.write( "3y=3<BR>\n" );
document.write( "y=1<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "a=1<BR>\n" );
document.write( "b=1.5<BR>\n" );
document.write( "10y+6b<BR>\n" );
document.write( "10*1+6*1.5<BR>\n" );
document.write( "10+9=19 km<BR>\n" );
document.write( "check<BR>\n" );
document.write( "9a+5x<BR>\n" );
document.write( "9+10=19<BR>\n" );
document.write( "ok\r<BR>\n" );
document.write( "\n" );
document.write( "We really only needed to solve for (a and x) or (b and y). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );