document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134473>Question 1134473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the boat. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751864 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let r = the speed of the boat in still water.<BR>\n" );
document.write( "let w = the speed of the water.\r<BR>\n" );
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document.write( "the general equaation in still water is r * t = d.\r<BR>\n" );
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document.write( "when the boat is going downstream, the general equation becomes (r + w) * t = d\r<BR>\n" );
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document.write( "when the boat is going upstream, the general equation becomes (r - w) * t = d\r<BR>\n" );
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document.write( "you are given that the speed of the boat in still water is 16 miles per hour.\r<BR>\n" );
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document.write( "the downstream equation becomes (16 + w) * t = d<BR>\n" );
document.write( "the upstream equaton becomes (16 - w) * t = d\r<BR>\n" );
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document.write( "you are given that the boat travels 15 miles downstream in the same time that it travels 9 miles upstream.\r<BR>\n" );
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document.write( "the downstream equation becomes (16 + w) * t = 15<BR>\n" );
document.write( "the upstream equation becomes (16 - w) * t = 9\r<BR>\n" );
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document.write( "simplify both equations to get:\r<BR>\n" );
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document.write( "16 * t + w * t = 15<BR>\n" );
document.write( "16 * t - w * t = 9\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "2 * w * t = 6\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "w * t = 3\r<BR>\n" );
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document.write( "your original 2 equations of:\r<BR>\n" );
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document.write( "16 * t + w * t = 15<BR>\n" );
document.write( "16 * t - w * t = 9\r<BR>\n" );
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document.write( "become:\r<BR>\n" );
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document.write( "16 * t + 3 = 15<BR>\n" );
document.write( "16 * t - 3 = 9\r<BR>\n" );
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document.write( "subtract 3 from both sides of the first equation to get 16 * t = 12<BR>\n" );
document.write( "add 3 to both sides of the second equation to get 16 * t = 12\r<BR>\n" );
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document.write( "solve for t in both equations to get t = 12/16 in each equation.\r<BR>\n" );
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document.write( "simplify to get t = 3/4 in each equation.\r<BR>\n" );
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document.write( "go back to your two original equations of:\r<BR>\n" );
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document.write( "(16 + w) * t = 15<BR>\n" );
document.write( "(16 - w) * t = 9\r<BR>\n" );
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document.write( "replace t with 3/4 in these equations to get:\r<BR>\n" );
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document.write( "(16 + w) * 3/4 = 15<BR>\n" );
document.write( "(16 - w) * 3/4 = 9\r<BR>\n" );
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document.write( "simplify these equations to get:\r<BR>\n" );
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document.write( "12 + 3/4 * w = 15<BR>\n" );
document.write( "12 - 3/4 * w = 9\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "2 * 3/4 * w = 6\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "3/4 * w = 3\r<BR>\n" );
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document.write( "solve for w to get w = 4.\r<BR>\n" );
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document.write( "that's your solution\r<BR>\n" );
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document.write( "the speed of the water is 4 miles per hour.\r<BR>\n" );
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document.write( "going downstream, the equation of (16 + w) * t = 15 becomes (16 + 4) * 3/4 = 15 which becomes 20 * 3/5 = 15 which becomes 15 = 15 which is true.\r<BR>\n" );
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document.write( "going upstream, the equation of (16 - w) * t = 9 bercomes (16 - 4) * 3/4 = 9 which  becomes 12 * 3/4 = 9 which becomes 9 = 9 which is true.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "the solution is that the speed of the water is 4 miles per hour.\r<BR>\n" );
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document.write( "in addition, we have solved for the time to be equal to 3/4 of an hour.\r<BR>\n" );
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document.write( "it is also posible to solve for w without first solving for t.\r<BR>\n" );
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document.write( "that could be done as follows:\r<BR>\n" );
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document.write( "your original equations to be solved are:\r<BR>\n" );
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document.write( "(16 + w) * t = 15<BR>\n" );
document.write( "(16 - w) * t = 9\r<BR>\n" );
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document.write( "solve for t in both equations to get:\r<BR>\n" );
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document.write( "t = 15 / (16 + w) and t = 9 / (16 - w)\r<BR>\n" );
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document.write( "since t = t, then 15 / (16 + w) = 9 / (16 - w)\r<BR>\n" );
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document.write( "multiply both sides of this equation by (16 + w) * (16 - w) to get:\r<BR>\n" );
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document.write( "15 * (16 - w) = 9 * (16 + w)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "15 * 16 - 15 * w = 9 * 16 + 9 * w\r<BR>\n" );
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document.write( "add 15 * w to both sides of this equation and subtract 9 * 16 from both sides of this equation to get:\r<BR>\n" );
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document.write( "15 * 16 - 9 * 16 = 9 * w + 15 * w\r<BR>\n" );
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document.write( "simplify further to get 96 = 24 * w\r<BR>\n" );
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document.write( "solve for w to get w = 96 / 24 = 4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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