document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194837>Question 194837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Zene decides to canoe 6 miles upstream on a river to a waterfall and back. The total trip is 8 hours. She can canoe an average of 3 miles per hour. What is the speed of the current? I would like more than just the answer, need to know how to get the answer. Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146198 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=146198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <b><i>r</i></b> represent the rate of the current.  Then <b>3 - <i>r</i></b> is the rate of the boat going upstream and <b>3 + <i>r</i></b> is the rate of the boat going downstream.  Then let <b><i>t</i></b> be the time taken to go upstream which means that the time to go downstream must be <b>8 - <i>t</i></b>\r<BR>\n" );
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document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE d = rt\">, the upstream trip is then described by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6 = (3 - r)t\">\r<BR>\n" );
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document.write( "And the downstream trip is described by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6 = (3 + r)(8 - t)\">\r<BR>\n" );
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document.write( "Solve each of these equations for <b><i>t</i></b>.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{6}{3 - r}\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8 - t = \frac{6}{3 + r}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = 8 - \frac{6}{3 + r}\">\r<BR>\n" );
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document.write( "Now we have two expressions equal to <b><i>t</i></b>, so set them equal to each other:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8 - \frac{6}{3 + r} = \frac{6}{3 - r}\">\r<BR>\n" );
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document.write( "Put everything on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8 - \frac{6}{3 + r} - \frac{6}{3 - r} = 0\">\r<BR>\n" );
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document.write( "LCD is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (3 + r)(3 - r) = 9 - r^2\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{8(9-r^2)-6(3-r)-6(3+r)}{9-r^2} = 0\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 9 - r^2\"> to get rid of the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8(9-r^2)-6(3-r)-6(3+r) = 0\">\r<BR>\n" );
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document.write( "Remove parentheses and collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 72 - 8r^2 - 18 + 6r - 18 - 6r = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -8r^2 + 36 = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r^2 = \frac{36}{8}\">\r<BR>\n" );
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document.write( "Only consider the positive root because we are reasonably certain that the current never went backwards during this trip, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r = \sqrt{\frac{36}{8}} = \frac{6}{2\sqrt{2}} = \frac{3}{\sqrt{2}} = \frac{3\sqrt{2}}{2}\">\r<BR>\n" );
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document.write( "Checking the answer is left as an exercise for the student.\r<BR>\n" );
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document.write( "John<BR>\n" );
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