document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189181>Question 1189181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two kayakers paddle 18 km downstream with the current in the same time it takes them to go 8 km upstream against the current. The rate of the current is 3 km/hr. What is the rate of the kayakers in still water?\r<BR>\n" );
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document.write( "Fill in the details:\r<BR>\n" );
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document.write( "Downstream:  Distance (km)?  Rate (km/hr)?  Time (hr)<BR>\n" );
document.write( "Upstream: Distance (km)?  Rate (km/hr)?  Time (hr) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820458 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820458\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "As suggested by the way the problem is posted, all three of the responses you have received to this point use some form of the standard equation<br><BR>\n" );
document.write( "time = distance/rate<br><BR>\n" );
document.write( "knowing that the times upstream and downstream are the same.<br><BR>\n" );
document.write( "rate of kayaker: x<BR>\n" );
document.write( "upstream rate: x-3<BR>\n" );
document.write( "downstream rate: x+3<br><BR>\n" );
document.write( "The time for 18km downstream is the same as the time for 8km upstream:<br><BR>\n" );
document.write( "18/(x+3)=8(x-3)<BR>\n" );
document.write( "etc...<br><BR>\n" );
document.write( "Here is a different approach that I personally find easier for problems like this.<br><BR>\n" );
document.write( "The times are the same, so the ratio of distances is the same as the ratio of rates.<br><BR>\n" );
document.write( "The ratio of distances is 18:8, or 9:4, so let the two rates be 9x and 4x.<br><BR>\n" );
document.write( "The difference between those two rates is 6km/h:<br><BR>\n" );
document.write( "9x-4x=6<BR>\n" );
document.write( "5x=6<BR>\n" );
document.write( "x=1.2<br><BR>\n" );
document.write( "The two rates are 9x=10.8km/h and 4x=4.8km/h; the rate of the kayaker is halfway between those two rates, 7.8km/h (i.e., 3km/h faster than 4.8km/h, and 3km/h slower than 10.8km/h).<br><BR>\n" );
document.write( "ANSWER: 7.8km/h<br><BR>\n" );
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