document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078376>Question 1078376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cyclists travel 210 miles. One cyclist, traveling 10 mph faster than the second cyclist, covers the distance in 2.4 hours less than the second cyclist.  Find the rate of the first cyclist. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692866 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=692866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two cyclists travel 210 miles.<BR>\n" );
document.write( " One cyclist, traveling 10 mph faster than the second cyclist, covers the distance in 2.4 hours less than the second cyclist.<BR>\n" );
document.write( " Find the rate of the first cyclist. <BR>\n" );
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document.write( "let s = the speed of the 1st cyclist <BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-10) = the speed of the 2nd cyclist<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "2nd cyclist time - 1st cyclist time = 2.4 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F%28%28s-10%29%29 ALIGN=MIDDLE  ALT=\"210%2F%28%28s-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2Fs ALIGN=MIDDLE  ALT=\"210%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.4<BR>\n" );
document.write( "multiply equation by s(s-10)<BR>\n" );
document.write( "s(s-10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F%28%28s-10%29%29 ALIGN=MIDDLE  ALT=\"210%2F%28%28s-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - s(s-10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2Fs ALIGN=MIDDLE  ALT=\"210%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.4s(s-10)<BR>\n" );
document.write( "cancel denominators<BR>\n" );
document.write( "210s - 210(s-10) = 2.4s^2 - 24s<BR>\n" );
document.write( "210s - 210s + 2100 = 2.4s^2 - 24s<BR>\n" );
document.write( "arrange as a quadratic equation<BR>\n" );
document.write( "2.4s^2 - 24s - 2100 = 0<BR>\n" );
document.write( "simplify, divide by 2.4<BR>\n" );
document.write( "s^2 - 10s - 875 = 0<BR>\n" );
document.write( "You can use the quadratic formula; a=1; b=-10; c=-875, but this will factor<BR>\n" );
document.write( "(s+25)(s-35) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "s = 35 mph is speed of the 1st cyclist<BR>\n" );
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document.write( "Check this by finding the actual time of each cycle<BR>\n" );
document.write( "210/25 = 8.4 hrs the time of the 2nd cyclist<BR>\n" );
document.write( "210/35 = 6.0 hrs for the 1st cyclist<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "time dif:2.4 hrs\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );