document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=312076>Question 312076</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ride the peaks. Smith bicycled 45 miles going east from<BR>\n" );
document.write( "Durango, and Jones bicycled 70 miles. Jones averaged<BR>\n" );
document.write( "5 miles per hour more than Smith, and his trip took one-half<BR>\n" );
document.write( "hour longer than Smith’s. How fast was each one traveling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #223309 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=223309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles.<BR>\n" );
document.write( " Jones averaged 5 miles per hour more than Smith, and his trip took one-half<BR>\n" );
document.write( "hour longer than Smith’s.<BR>\n" );
document.write( " How fast was each one traveling?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = Smith's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = Jone's speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation, Time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Jones time - Smiths time = .5 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Fs ALIGN=MIDDLE  ALT=\"45%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5<BR>\n" );
document.write( "multiply by s(s+5), results:<BR>\n" );
document.write( "70s - 45(s+5) = .5s(s+5)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "70s - 45s - 225 = .5s^2 + 2.5s<BR>\n" );
document.write( "25s - 225 = .5s^2 + 2.5s<BR>\n" );
document.write( "combine on the right<BR>\n" );
document.write( "0 = .5s^2 + 2.5s - 25s + 225<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( ".5s^2 - 22.5s + 225 = 0<BR>\n" );
document.write( "Get rid of th decimals, mult by 2<BR>\n" );
document.write( "s^2 - 45s + 450 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s-15)(s-30) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "s = 15 mph is Smith's time, then Jones time = 20 mph<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = 30 mph is Smith's time, then Jones time = 35<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The slower time would make more sense for bicycle<BR>\n" );
document.write( "Check by finding the times<BR>\n" );
document.write( "70/20 = 3.5<BR>\n" );
document.write( "45/15 = 3.0<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "differ: .5h<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );