document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029727>Question 1029727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chris went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644774 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rt = d<BR>\n" );
document.write( "d = 24<BR>\n" );
document.write( "rt = 24\r<BR>\n" );
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document.write( "(r+6)(t-9) = 24<BR>\n" );
document.write( "simplify to get rt - 9r + 6t - 54 = 24\r<BR>\n" );
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document.write( "rt = 24<BR>\n" );
document.write( "solve for r to get r = 24/t\r<BR>\n" );
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document.write( "replace r with 24/t in the equation of rt - 9r + 6t - 54 = 24 to get:<BR>\n" );
document.write( "24t/t - 216/t + 6t - 54 = 24\r<BR>\n" );
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document.write( "multiply both sides of this equation by t to get:<BR>\n" );
document.write( "24t - 216 + 6t^2 - 54t = 24t\r<BR>\n" );
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document.write( "subtract 24t from both sides of this equation and combine like terms and reorder the terms in descending order of degree to get:<BR>\n" );
document.write( "6t^2 - 54t - 216 = 0\r<BR>\n" );
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document.write( "factor out the gcf  of 6 to get:<BR>\n" );
document.write( "t^2 - 9t - 36 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:<BR>\n" );
document.write( "(t-12)(t+3)\r<BR>\n" );
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document.write( "solve for t to get:<BR>\n" );
document.write( "t = 12 or t = -3<BR>\n" );
document.write( "t = -3 can't be good because time is not negative, so you get t = 12.\r<BR>\n" );
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document.write( "when t = 12, rt = 24 becomes r*12 = 24 and solve for r to get r = 2.\r<BR>\n" );
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document.write( "you have r = 2<BR>\n" );
document.write( "t = 12\r<BR>\n" );
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document.write( "rt = d becomes 2*12 = 24, confirming this is good.\r<BR>\n" );
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document.write( "r+6 = 8<BR>\n" );
document.write( "t-9 = 3\r<BR>\n" );
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document.write( "(r+6)(t-9) = d becomes 8*3 = 24, confirming this is also good.\r<BR>\n" );
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document.write( "your solution is that he was riding at 2 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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