document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085270>Question 1085270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Brian decides to start training for swimming in a river.  The current in the river is<BR>\n" );
document.write( "4km/hr.  If he swims upstream 2 km and then back downstream to where he started in 3<BR>\n" );
document.write( "hours, what is his swimming speed?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699370 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=699370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\">Let <BR>\n" );
document.write( "x = Brian's swimming speed in still water (no current)<BR>\n" );
document.write( "t1 = time it takes to swim against the current<BR>\n" );
document.write( "t2 = time it takes to swim with the current\r<BR>\n" );
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document.write( "Make a table to get<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Distance</TD><TD >Rate</TD><TD >Time</TD></tr><tr><TD >Against Current</TD><TD >2</TD><TD >x-4</TD><TD >t1</TD></tr><tr><TD >With Current</TD><TD >2</TD><TD >x+4</TD><TD >t2</TD></tr>\n" );
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document.write( "Against the current, we can say\r<BR>\n" );
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document.write( "d = r*t<BR>\n" );
document.write( "2 = (x-4)*t1<BR>\n" );
document.write( "t1 = 2/(x-4)\r<BR>\n" );
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document.write( "with the current, we can say\r<BR>\n" );
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document.write( "d = r*t<BR>\n" );
document.write( "2 = (x+4)*t2<BR>\n" );
document.write( "t2 = 2/(x+4)\r<BR>\n" );
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document.write( "The two time values (t1 and t2) add to 3 hours, so\r<BR>\n" );
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document.write( "t1 + t2 = 3<BR>\n" );
document.write( "2/(x-4) + 2/(x+4) = 3\r<BR>\n" );
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document.write( "Let's solve for x\r<BR>\n" );
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document.write( "2/(x-4) + 2/(x+4) = 3\r<BR>\n" );
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document.write( "[2/(x-4) + 2/(x+4)](x-4)(x+4) = 3(x-4)(x+4) ... <font color=blue>multiply both sides by (x-4)(x+4)</font>\r<BR>\n" );
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document.write( "2(x+4)+2(x-4) = 3(x-4)(x+4)\r<BR>\n" );
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document.write( "2x+8 + 2x-8 = 3(x^2-16)\r<BR>\n" );
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document.write( "4x = 3x^2-48\r<BR>\n" );
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document.write( "4x-4x = 3x^2-48-4x\r<BR>\n" );
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document.write( "0 = 3x^2-4x-48\r<BR>\n" );
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document.write( "3x^2-4x-48 = 0\r<BR>\n" );
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document.write( "Use a calculator or the quadratic formula to solve 3x^2-4x-48 = 0 to get the solution set {x = -3.388508353532, x = 4.721841686865} which are approximate values.\r<BR>\n" );
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document.write( "Toss out the negative x value because negative speeds don't make sense.\r<BR>\n" );
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document.write( "The only practical solution is approximately <font color=red>4.721841686865</font> which is the final answer. The units are in km per hour.\r<BR>\n" );
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document.write( "So this means that Brian's speed in still water (with no current) is approximately 4.721841686865 km/hr.</font> </SPAN>\n" );
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