document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761492>Question 761492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 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 #463252 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=463252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.<BR>\n" );
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document.write( "Sue DATA:<BR>\n" );
document.write( "distance = 154 miles ; time = x-3 hrs ; rate = d/t = 154/(x-3) mph<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Doreen DATA:<BR>\n" );
document.write( "distance = 70 miles ; time = x hrs ; rate = 70/x mph<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "rate - rate = 15 mph<BR>\n" );
document.write( "154/(x-3) - 70/x = 15<BR>\n" );
document.write( "154x - 70(x-3)=15x(x-3)<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "154x - 70x + 210 = 15x^2 - 15x<BR>\n" );
document.write( "84x + 210 = 15x^2 - 15x<BR>\n" );
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document.write( "15x^2 - 99x - 210 = 0<BR>\n" );
document.write( "5x^2 - 33x - 70 = 0<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "x = 8.89  hrs (Doreen time) ; 70/8.289 = 8.445 mph (Doreen rate)<BR>\n" );
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document.write( "x-3 = 5.89 hrs (Sue time) ; 154/5.89 = 18.24 mph (Sue rate)<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=================== </SPAN>\n" );
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