document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998576>Question 998576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in six hours A walks 10 kilometers more than B in five hours and in 8 hours B walks 7 kilometers more than A does in 5 hours what are the speeds of each person? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616339 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call their rates A and B.  The equations become (since rate times time = distance):<BR>\n" );
document.write( "6A - 5B = 10<BR>\n" );
document.write( "8B - 5A = 7 (or -5A + 8B = 7)<BR>\n" );
document.write( "Now solve this system of equations...multiply appropriately to get<BR>\n" );
document.write( "30A - 25B = 50<BR>\n" );
document.write( "-30A + 48B = 42<BR>\n" );
document.write( "When we add these we get<BR>\n" );
document.write( "23B = 92 and<BR>\n" );
document.write( "B = 4 km/hr<BR>\n" );
document.write( "A can be found by substituting into the first equation<BR>\n" );
document.write( "6A - 5(4) = 10<BR>\n" );
document.write( "6A = 30<BR>\n" );
document.write( "A = 5 km/hr </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );