document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068609>Question 1068609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A paddle boat can move at a speed of 8 km/h in still water. The boat is paddled 4 km downstream in a river in the same time it takes to go 2 km upstream. What is the speed of the river? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683897 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52777)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A paddle boat can move at a speed of 8 km/h in still water. The boat is paddled 4 km downstream in a river in the same time <BR>\n" );
document.write( "it takes to go 2 km upstream. What is the speed of the river?<BR>\n" );
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document.write( "Let \"v\" be the speed of the river (or, better to say, current rate), in km/h.\r\n" );
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document.write( "Then the speed of the boat downstream is (8+v) km/h (relative to the river banks),\r\n" );
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document.write( "and  the speed of the boat downstream is (8-v) km/h.\r\n" );
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document.write( "Therefore, the time for traveling 4 km downstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%288%2Bv%29 ALIGN=MIDDLE  ALT=\"4%2F%288%2Bv%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours,\r\n" );
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document.write( "and        the time for traveling 2 km   upstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%288-v%29 ALIGN=MIDDLE  ALT=\"2%2F%288-v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.\r\n" );
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document.write( "According to the condition, time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%288%2Bv%29 ALIGN=MIDDLE  ALT=\"4%2F%288%2Bv%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%288-v%29 ALIGN=MIDDLE  ALT=\"2%2F%288-v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which gives you an equation\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%288%2Bv%29 ALIGN=MIDDLE  ALT=\"4%2F%288%2Bv%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%288-v%29 ALIGN=MIDDLE  ALT=\"2%2F%288-v%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.    (1)\r\n" );
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document.write( "It is your equation to find the unknown \"v\". To solve it, multiply both sides of (1) by (8+v)*(8-v). You will get\r\n" );
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document.write( "4*(8-v) = 2*(8+v).\r\n" );
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document.write( "Simplify and solve for v:\r\n" );
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document.write( "32 - 4v = 16 + 2v  --->  32 - 16 = 2v + 4v  --->  6v = 16  --->  v = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F6 ALIGN=MIDDLE  ALT=\"16%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h.\r\n" );
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document.write( "<U>Answer</U>.  The current rate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h.\r\n" );
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document.write( "<U>Check</U>.  Speed downstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B+8%2F3 ALIGN=MIDDLE  ALT=\"8%2B+8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824%2B8%29%2F3 ALIGN=MIDDLE  ALT=\"%2824%2B8%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2F3 ALIGN=MIDDLE  ALT=\"32%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h;  Time downstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28%2832%2F3%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28%2832%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2A3%29%2F32 ALIGN=MIDDLE  ALT=\"%284%2A3%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F32 ALIGN=MIDDLE  ALT=\"12%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > of an hour.\r\n" );
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document.write( "        Speed   upstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-+8%2F3 ALIGN=MIDDLE  ALT=\"8-+8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2824-8%29%2F3 ALIGN=MIDDLE  ALT=\"%2824-8%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h;  Time   upstream is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%2816%2F3%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%2816%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A3%29%2F16 ALIGN=MIDDLE  ALT=\"%282%2A3%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F16 ALIGN=MIDDLE  ALT=\"6%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > of an hour. \r\n" );
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document.write( "Solved and checked.\r<BR>\n" );
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document.write( "It is a typical and standard Upstream and Downstream trip word problem.\r<BR>\n" );
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document.write( "You can find many similar fully solved problems on upstream and downstream trips with detailed solutions in lessons \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Read them attentively and learn how to solve this type of problems once and for all.\r<BR>\n" );
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the section \"<U>Word problems</U>\", the topic \"<U>Travel and Distance problems</U>\".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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