document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158338>Question 158338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man takes 1 hour to row 2km upstream and return. The river has a current of 2kph. Find the speed of the man 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 #116731 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=rate (speed) of the man in still water\r<BR>\n" );
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document.write( "Time to travel upstream =2/(r-2) (upstream we need to subtract the speed of the current)<BR>\n" );
document.write( "Time to travel downstream=2/(r+2) (downstream we add the speed of the current)\r<BR>\n" );
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document.write( "Now we are told that the above two times add up to 1 hour, so:\r<BR>\n" );
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document.write( "2/(r-2) + 2/r+2)=1  multiply each term by (r-2)(r+2)<BR>\n" );
document.write( "2(r+2)+2(r-2)=(r-2)(r+2)  get rid of parens\r<BR>\n" );
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document.write( "2r+4 +2r-4=r^2-4 or<BR>\n" );
document.write( "4r=r^2-4  subtract 4r from each side\r<BR>\n" );
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document.write( "r^2-4r-4=0 quadratic in standard form; solve using the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%284%2B-+sqrt%28%28-4%29%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"r+=+%284%2B-+sqrt%28%28-4%29%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%284%2B-+sqrt%2816%2B16+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"r+=+%284%2B-+sqrt%2816%2B16+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%284%2B-+sqrt%2832+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"r+=+%284%2B-+sqrt%2832+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%284%2B-+5.66%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"r+=+%284%2B-+5.66%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "We will discount the negative value for r; speed in this problem is positive<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%284%2B5.66%29%2F2=9.66%2F2=4.83 ALIGN=MIDDLE  ALT=\"r=%284%2B5.66%29%2F2=9.66%2F2=4.83\"   DISABLED_style= \"max-width:90%; height:auto;\" > kph---speed of man in still water<BR>\n" );
document.write( "2/(4.83-2) +2/(4.83+2)=1<BR>\n" );
document.write( "2/2.83 +2/6.83=1<BR>\n" );
document.write( "0.707+0.293=1<BR>\n" );
document.write( "1=1\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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