document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=294627>Question 294627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One day, Jeff rides his bicycle out into the country 40 miles (see figure). On the way back, he takes a different route that is 2 miles longer. It takes him 6 hours longer to ride out than to return. If his rate on the way out into the country is 16 miles per hour slower than his rate back, find both rates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212526 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=212526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One day, Jeff rides his bicycle out into the country 40 miles (see figure).<BR>\n" );
document.write( " On the way back, he takes a different route that is 2 miles longer.<BR>\n" );
document.write( " It takes him 6 hours longer to ride out than to return.<BR>\n" );
document.write( "If his rate on the way out into the country is 16 miles per hour slower than<BR>\n" );
document.write( " his rate back, find both rates.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = his speed into the country<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+16) = his return speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation, Time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "out time - return time = 6 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fs ALIGN=MIDDLE  ALT=\"40%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%2F%28%28s%2B16%29%29 ALIGN=MIDDLE  ALT=\"42%2F%28%28s%2B16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
document.write( "Multiply equation by s(s+16) to eliminate the denominators, results<BR>\n" );
document.write( "40(s+16) - 42s  = 6s(s+16)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "40s + 640 - 42s = 6s^2 + 96s<BR>\n" );
document.write( ";<BR>\n" );
document.write( "640 - 2s = 6s^2 + 96s<BR>\n" );
document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = 6s^2 + 96s + 2s - 640<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "6s^2 + 98s - 640 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "3s^2 + 49s - 320 = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(3s + 64)(s - 5) = 0<BR>\n" );
document.write( "the positive solution is what we want here<BR>\n" );
document.write( "s = 5 mph his outbound rate<BR>\n" );
document.write( "and<BR>\n" );
document.write( "5 + 16 = 21 mph his return rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by finding the times<BR>\n" );
document.write( "40/5 = 8 hrs<BR>\n" );
document.write( "42/21 = 2 hrs<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "diff: 6 hrs<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );