document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182578>Question 182578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The speed of a stream is 5mph. If a boat travels 66 miles down stream in the same time that it takes to travel 33 miles upstream. What is the speed of the boat in still water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137069 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=137069\">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( "Relative to the bank of the river, the boat travels the speed in still water <i><b>plus</b></i> the speed of the current when going downstream, and speed in still water <i><b>minus</b></i> the speed of the current when going upstream.\r<BR>\n" );
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document.write( "The speed of the current is 5 mph, so if the speed of the boat in still water is <i>r</i>, the downstream speed is <i>r</i> + 5, and the upstream speed is <i>r</i> - 5.\r<BR>\n" );
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document.write( "Since distance equals rate times time, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d = rt\">, we also know that time equals distance divided by rate, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t = \frac{d}{r}\">.\r<BR>\n" );
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document.write( "So the time for the downstream trip must be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math t = \frac{66}{r + 5}\">\r<BR>\n" );
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document.write( "While the time for the upstream trip must be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math t = \frac{33}{r - 5}\">\r<BR>\n" );
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document.write( "But these times are equal so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{66}{r + 5} = \frac{33}{r - 5}\">\r<BR>\n" );
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document.write( "Giving us a simple proportion.  Cross-multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 66(r - 5) = 33(r + 5)\">\r<BR>\n" );
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document.write( "Divide both sides by 33:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2(r - 5) = r + 5\">\r<BR>\n" );
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document.write( "Distribute and collect:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2r - r = 5 + 10\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math r = 15\">\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" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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