document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039010>Question 1039010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It  takes 5 days for a steamboat to travel from A to B along a <BR>\n" );
document.write( "river. It takes 7 days to return from B to A. How many days will <BR>\n" );
document.write( "it take for a raft to drift from A to B (all speeds stay constant)?\r<BR>\n" );
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document.write( "(1) 13<BR>\n" );
document.write( "(2) 35<BR>\n" );
document.write( "(3) 6<BR>\n" );
document.write( "(4) 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653734 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=653734\">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( "Let the rate of the steamboat be represented by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> and the rate of the current be represented by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_c\">.  Since the trip from A to B takes less time than from B to A, the boat must be going with the current.  That means that the total speed of the boat with respect to the bank of the river is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ +\ r_c\">.  Likewise, going back upstream, the speed is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ -\ r_c\">.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> represent the distance from A to B.  One assumes that A and B are fixed points so that the distance remains constant regardless of the direction of travel.  We know that distance equals rate times time, so the downstream trip is modeled by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5(r\ +\ r_c)\">\r<BR>\n" );
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document.write( "and the upstream trip by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 7(r\ -\ r_c)\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ d\">, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 7(r\ -\ r_c)\ =\ 5(r\ +\ r_c)\">\r<BR>\n" );
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document.write( "Solving:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ 6r_c\">\r<BR>\n" );
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document.write( "And substituting into the model for the downstream trip:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5(6r_c\ +\ r_c)\ =\ 5(7r_c)\ =\ 35r_c\">\r<BR>\n" );
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document.write( "Dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r_c\"> we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{r_c}\ =\ 35\">\r<BR>\n" );
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document.write( "And since time is equal to distance divided by rate, we have our answer.\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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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