document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=872957>Question 872957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tatiana takes a 40 mile round trip bicycle trip and travels at a a constant speed the entire. On the first leg of the trip, she is riding against the wind, which is blowing at a constant rate of 3 miles per hour. On her return trip, she is riding with the wind. She starts the bike ride at 11:30 am and ends at 3:30 pm. How fast would Tatiana ride her bike on an absolutely windless day? If necessary, round your answers to the nearest hundredth.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #526546 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=526546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tatiana takes a 40 mile round trip bicycle trip and travels at a a constant speed the entire. On the first leg of the trip, she is riding against the wind, which is blowing at a constant rate of 3 miles per hour. On her return trip, she is riding with the wind. She starts the bike ride at 11:30 am and ends at 3:30 pm. How fast would Tatiana ride her bike on an absolutely windless day? If necessary, round your answers to the nearest hundredth. <BR>\n" );
document.write( "------<BR>\n" );
document.write( "1st leg DATA:<BR>\n" );
document.write( "dist = 20 miles ; rate = r-3 mph ; time = d/r = 20/(r-3) hrs<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2nd leg DATA:<BR>\n" );
document.write( "dist = 20 miles ; rate = r+3 mph ; time = d/r = 20/(r+3) hrs<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "time + time = 4 hrs<BR>\n" );
document.write( "20/(r-3) + 20/(r+3) = 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "20(r+3) + 20(r-3) = 4(r^2-9)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "40r = 4r^2 - 36<BR>\n" );
document.write( "----<BR>\n" );
document.write( "r^2 - 10r - 9 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "r = [10 +- sqrt(100-4*-9)]/2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "r = [10 +- sqrt(136)]/2<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "r = 10.83 mph (rate in still air)<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" );