document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248643>Question 248643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45 mi downstream in a total time of 8 hours. 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 #181203 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45 mi downstream in a total time of 8 hours. What is the speed of the boat in still water?\r<BR>\n" );
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document.write( "Distance traveled = speed(rate) * time traveled or D = R*T\r<BR>\n" );
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document.write( "Let X be the speed of the boat in still water.<BR>\n" );
document.write( "Let T be the time taken to go upstream.<BR>\n" );
document.write( "Then 8-T is the time taken to go downstream.\r<BR>\n" );
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document.write( "We then have two equations in two unknowns as follows:\r<BR>\n" );
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document.write( "(1.) (X-3)*T = 45<BR>\n" );
document.write( "(2.) (X+3)*(8-T) = 45\r<BR>\n" );
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document.write( "Solve the first equation for T. \r<BR>\n" );
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document.write( "T=45/(X-3)\r<BR>\n" );
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document.write( "Substitute this value for T in the second equation:\r<BR>\n" );
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document.write( "(X+3)*(8-T)<BR>\n" );
document.write( "(X+3)*(8-(45/(X-3)) = 45\r<BR>\n" );
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document.write( "Expand:\r<BR>\n" );
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document.write( "(8*X)-(45*X/(X-3)) + 24 - 135/((X-3) = 45\r<BR>\n" );
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document.write( "Multiply both sides by (X-3):\r<BR>\n" );
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document.write( "(8*X)*(X-3) - 45*X + 24*(X-3) - 135 = 45*(X-3)\r<BR>\n" );
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document.write( "Expand:\r<BR>\n" );
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document.write( "8*X^2 - 24*X -45*X + 24*X - 72 - 135 = 45*X - 135\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "8*X^2 -90*X - 72 = 0\r<BR>\n" );
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document.write( "Divide both sides by 2:\r<BR>\n" );
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document.write( "4*X^2 - 45*X - 36 = 0\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "(4X+3) * (X-12) = 0\r<BR>\n" );
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document.write( "Solve for Positive X.  \r<BR>\n" );
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document.write( " </SPAN>\n" );
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