document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148759>Question 148759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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 ½ hour longer than Smith’s. How fast was each one travelling?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109103 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=109103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Smith bicycled 45 miles going east from Durango<BR>\n" );
document.write( "Smith DATA:<BR>\n" );
document.write( "distance = 45 miles ; rate = x mph : time = d/r = 45/x hrs.<BR>\n" );
document.write( " and Jones bicycled 70 miles.<BR>\n" );
document.write( "Jones DATA:<BR>\n" );
document.write( "distance = 70 miles ; rate = (x+5) mph ; time = d/r = 70/(x+5) hrs. <BR>\n" );
document.write( "Jones averaged 5 miles per hour more than Smith and his trip took ½ hour longer than Smith’s. <BR>\n" );
document.write( "How fast was each one traveling? <BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "Jones time - Smith time = 1/2<BR>\n" );
document.write( "45/x - 70/(x+5) = 1/2<BR>\n" );
document.write( "90(x+5) - 140x = x^2+5x<BR>\n" );
document.write( "-50x + 450 = x^2 + 5x<BR>\n" );
document.write( "x^2 + 60x - 450 = 0<BR>\n" );
document.write( "x = [-60 +-sqrt(60^2-4*-450)]/2<BR>\n" );
document.write( "x = [-60 +- sqrt(5400)]/2<BR>\n" );
document.write( "Positive Solution<BR>\n" );
document.write( "x = (-60+ 73.48)/2<BR>\n" );
document.write( "x = 13.48/2 = 6.74 mph (Smith's rate)<BR>\n" );
document.write( "x+5 = 11.74 mph (Jones's rate)<BR>\n" );
document.write( "==========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------------------ </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );