document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948114>Question 948114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To travel 110 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 72 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578640 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=578640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To travel 110 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 72 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.<BR>\n" );
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document.write( "Doreen DATA:<BR>\n" );
document.write( "dist = 72 miles ; time = x hrs ; rate = d/t = 72/x mph<BR>\n" );
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document.write( "Sue DATA:<BR>\n" );
document.write( "dist = 110 miles ; time = x-3 hrs ; rate = d/t = 110/(x-3) mph<BR>\n" );
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document.write( "Equation::<BR>\n" );
document.write( "Sue = Doreen + 13 <BR>\n" );
document.write( "110/(x-3) = [72/x] + 13<BR>\n" );
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document.write( "110x = 72(x-3) + 13x(x-3)<BR>\n" );
document.write( "110x = 72x - 216 + 13x^2 - 39x<BR>\n" );
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document.write( "38x = -216 + 13x^2 - 39x<BR>\n" );
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document.write( "13x^2 -77x -216 = 0<BR>\n" );
document.write( "Positive solution::<BR>\n" );
document.write( "x = 8 <BR>\n" );
document.write( "Doreen rate = 72/8 = 9 mph<BR>\n" );
document.write( "Sue rate = 110/(8-3) = 22 mph<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "--------- </SPAN>\n" );
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