document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277650>Question 277650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202102 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man bicycles 5.4 mph faster than he can walk. He bicycles a distance of 32.4 miles and then hikes back along the same route. If the entire trip takes 12.6 hours, how fast does he walk?<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Let his walking rate be w mph<BR>\n" );
document.write( "Then his biking rate is w+5.4 mph<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Bike DATA:<BR>\n" );
document.write( "distance = 32.4 mi; rate = (w+5.4) mph ; time = d/r = 32.4/(w+5.4)hrs.<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "Walk DATA:<BR>\n" );
document.write( "distance = 32.4 mi ; rate = w mph ; time = d/r = 32.4/w hrs.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "time + time = 12.6 hrs<BR>\n" );
document.write( "32.4/(w+5.4) + 32.4/w = 12.6<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Multiply thru by 10:<BR>\n" );
document.write( "324/(w+5.4) + 324/w = 126<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Multiply thru by w(w+5.4) to get:<BR>\n" );
document.write( "324w + 324(w+5.4) = 126w(w+5.4)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "648w + 1749.6 = 126w^2 + 680.4w<BR>\n" );
document.write( "---<BR>\n" );
document.write( "126w^2 + 32.4w - 1749 = 0<BR>\n" );
document.write( "w = -3.599 or w = 3.857<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "walking rate = 3.857 mph<BR>\n" );
document.write( "==================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );