document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995694>Question 995694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem: (show all working out please, Thanks)\r<BR>\n" );
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document.write( "In a race over 4km Ryan ran at a constant speed. However, Sophie ran at the first 2 km at a speed of 1km/h more than Ryan and ran the second 2km at a speed of 1km/h less than Ryan. Who won the race? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614386 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=614386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ryan runs faster.\r<BR>\n" );
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document.write( "here's my worksheet that confirms it for all ryan rates that are valid.\r<BR>\n" );
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document.write( "in this workbook:\r<BR>\n" );
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document.write( "x represnet ryans rate per kilometer.\r<BR>\n" );
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document.write( "the results are valid for all of ryan's rates greater than 1 kmph.\r<BR>\n" );
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document.write( "at 1 kmph, the results are not valid because there is a division by 0.\r<BR>\n" );
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document.write( "at less than 1 kmph, the results are invalid because sophie's rates becomes negative.\r<BR>\n" );
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document.write( "the formulas used are:\r<BR>\n" );
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document.write( "let x = ryan's rate.\r<BR>\n" );
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document.write( "rate * time = distance\r<BR>\n" );
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document.write( "distance = 4 km.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "x * time = 4\r<BR>\n" );
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document.write( "ryan's time = 4 / x\r<BR>\n" );
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document.write( "sophie's time is calculated as follows:\r<BR>\n" );
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document.write( "sophie's time for first 2 km is equal to 2 / (x+1)\r<BR>\n" );
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document.write( "sophie's time for second 2 km is equal to 2 / (x-1)\r<BR>\n" );
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document.write( "sophie's time for all 4 km is 2/(x+1) + 2/(x-1)\r<BR>\n" );
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document.write( "results are shown below:\r<BR>\n" );
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document.write( "div/0 means the results are invalid because there has been a division by 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/101101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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