document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=452380>Question 452380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip<BR>\n" );
document.write( "was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate<BR>\n" );
document.write( "walking, what was each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #310982 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=310982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man rode a bicycle for 12 miles and then hiked an additional 8 miles.<BR>\n" );
document.write( " The total time for the trip was 5 hours.<BR>\n" );
document.write( " If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = his walking rate<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+10) = his biking rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "walk time + biking time = 5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fs ALIGN=MIDDLE  ALT=\"8%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s%2B10%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by s(s+10)<BR>\n" );
document.write( "8(s+10) + 12s = 5s(s+10)<BR>\n" );
document.write( "8s + 80 + 12s = 5s^2 + 50s<BR>\n" );
document.write( "20s + 80 = 5s^2 + 50s<BR>\n" );
document.write( "0 = 5s^2 + 50s - 20s - 80 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "5s^2 + 30s - 80 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Simplify, divide by 5<BR>\n" );
document.write( "s^2 + 6s - 16 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(s+8)(s-2) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "s = 2 mph walking speed<BR>\n" );
document.write( "then, obviously:<BR>\n" );
document.write( "12 mph biking speed<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check that in the time equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F2 ALIGN=MIDDLE  ALT=\"8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F12 ALIGN=MIDDLE  ALT=\"12%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 hrs<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );