document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964015>Question 964015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jan and Tariq took a canoeing trip, traveling 6 mi upstream against a 2-mi/h current. They then returned to the same point downstream. If their entire trip took 4 hr, how fast could they paddle 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 #589036 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the formula, rate * time = distance<BR>\n" );
document.write( "Set x = speed in still water<BR>\n" );
document.write( "(x-2) * t1 = 6 miles<BR>\n" );
document.write( "(x+2) * t2 = 6 miles<BR>\n" );
document.write( "t1, the time paddling upstream  = distance 6 miles/ rate (x-2) or<BR>\n" );
document.write( "6/(x-2)<BR>\n" );
document.write( "t2, the time paddling downstream  = distance 6 miles/ rate (x+2) or<BR>\n" );
document.write( "6/(x+2)<BR>\n" );
document.write( "t1 + t2 = 4 hours, so<BR>\n" );
document.write( "6/(x-2) + 6/(x+2) = 4<BR>\n" );
document.write( "A common denominator is (x-2)(x+2) so we want<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28x-2%29%2A%28x%2B2%29%2F%28x%2B2%29+%2B+6%2F%28x%2B2%29%2A%28x-2%29%2F%28x-2%29+=+4 ALIGN=MIDDLE  ALT=\"6%2F%28x-2%29%2A%28x%2B2%29%2F%28x%2B2%29+%2B+6%2F%28x%2B2%29%2A%28x-2%29%2F%28x-2%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "expanding<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x+%2B+12+%2B+6x+-12%29%2F%28x%5E2-4%29+=+4%2F1 ALIGN=MIDDLE  ALT=\"%286x+%2B+12+%2B+6x+-12%29%2F%28x%5E2-4%29+=+4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%29%2F%28x%5E2-4%29+=+4%2F1 ALIGN=MIDDLE  ALT=\"%2812x%29%2F%28x%5E2-4%29+=+4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "do cross products<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x=4%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"12x=4%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x=4x%5E2-16 ALIGN=MIDDLE  ALT=\"12x=4x%5E2-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-12x-16 ALIGN=MIDDLE  ALT=\"0=4x%5E2-12x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide by 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-3x-4 ALIGN=MIDDLE  ALT=\"0=x%5E2-3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factoring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28x-4%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"0+=+%28x-4%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So possible values for x are 4 and -1<BR>\n" );
document.write( "Since we need a positive speed, the speed in<BR>\n" );
document.write( "still water is 4 mph </SPAN>\n" );
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