document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58754>Question 58754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one half hour longer than Smith’s.  How fast was each one traveling. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40365 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=40365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ride the peaks. Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one half hour longer than Smith’s. How fast was each one traveling.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "That Smith is going east from Durango does not seem to have any bearing on the <BR>\n" );
document.write( "problem.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Time = dist/speed;<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = Smith's speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Smith's time = 45/s<BR>\n" );
document.write( "Jones's time = 70/(s+5)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Smith's time + 1/2 hr = Jone's time <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Fs++%2B+.5 ALIGN=MIDDLE  ALT=\"45%2Fs++%2B+.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28s%2B5%29 ALIGN=MIDDLE  ALT=\"70%2F%28s%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Mult equation by s(s+5) and eliminate the denominators, then you have:<BR>\n" );
document.write( "45(s+5) + .5(s(s+5) = 70s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "45x + 225 + .5s^2 + 2.5s = 70s<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".5s^2 + 45s + 2.5s - 70s + 225 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".5s^2 - 22.5s + 225 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Mult eq by 2 and get rid of these decimals<BR>\n" );
document.write( "s^2 - 45s + 450 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(s - 15)(s - 30) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "s = 15; and s = 30; I'm not sure, but 30 seems fast for a bike to average for<BR>\n" );
document.write( "that distance. I'm going to say Smith's speed = 15 mph & Jones speed = 20 mph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check it: Jones time - Smiths time = .5hr<BR>\n" );
document.write( "70/20 - 45/15 =<BR>\n" );
document.write( "3.5 - 3 = .5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The other solution, s = 30:<BR>\n" );
document.write( "70/35 - 45/30 =<BR>\n" );
document.write( "2 - 1.5 = .5 also\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );