document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998631>Question 998631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carmen recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 5 miles per hour faster than on her way home. If Carmen spent a total of 2 hours bicycling, find the two rates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616400 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=616400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Carmen recently rode her bicycle to visit her friend who lives 12 miles away.<BR>\n" );
document.write( " On her way there, her average speed was 5 miles per hour faster than on her way home.<BR>\n" );
document.write( " If Carmen spent a total of 2 hours bicycling, find the two rates.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = speed on the way home<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = speed on the way there<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "time there + return time = 2 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fs ALIGN=MIDDLE  ALT=\"12%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "multiply equation by s(s+5), cancel the denominators and you have<BR>\n" );
document.write( "12s + 12(s+5) = 2s(s+5)<BR>\n" );
document.write( "12s + 12s + 60 = 2x^2 + 10s<BR>\n" );
document.write( "24s + 60 = 2s^2 + 10s<BR>\n" );
document.write( "arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 2s^2 + 10s - 24s - 60<BR>\n" );
document.write( "2s^2 - 14s -60 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "s^2 - 7s - 30 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s-10)(s+3) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "s = 10 mph her return speed<BR>\n" );
document.write( "then obviously,<BR>\n" );
document.write( "15 mph is the to speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that checks out, find the actual time each way<BR>\n" );
document.write( "12/15 = .8 hrs<BR>\n" );
document.write( "12/10 = 1.2 hrs<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "total time: 2 hrs </SPAN>\n" );
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