document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=513707>Question 513707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a barge move 6km/h in still water. it travels 15 km upstream and 15 km downstream in a total time of 9 h. what is teh speed of the current </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343111 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=343111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Time equals distance divided by rate.  The downstream rate is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6\ +\ r_c\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_c\"> is the speed of the current.  The upstream rate is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 6\ -\ r_c\">.  If we let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> represent the amount of time to go downstream, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 9\ -\ t\"> must represent the amount of time to go upstream.\r<BR>\n" );
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document.write( "Downstream trip:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{15}{6\ +\ r_c}\ =\ t\">\r<BR>\n" );
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document.write( "Upstream trip:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{15}{6\ -\ r_c}\ =\ 9\ -\ t\">\r<BR>\n" );
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document.write( "Substituting:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{15}{6\ -\ r_c}\ =\ 9\ -\ \frac{15}{6\ +\ r_c}\"> \r<BR>\n" );
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document.write( "Then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{15}{6\ -\ r_c}\ +\ \frac{15}{6\ +\ r_c}\ =\ 9\">\r<BR>\n" );
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document.write( "The lowest common denominator is the product of the two conjugate denominators, hence the difference of two squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 15(6\ +\ r_c)\ +\ 15(6\ -\ r_c)\ =\ 9(36\ -\ {r_c}^2)\">\r<BR>\n" );
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document.write( "A little Algebra Music, Maestro (verification left as an exercise for the student):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9{r_c}^2\ =\ 144\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_c\">.  Discard the negative root.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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