document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=318787>Question 318787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pontoon boat moves 6 km/h in still water. It travels 30 km upriver and 30 km downriver in total time of 18 hrs. What is the speed of the current? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228197 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=228197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A pontoon boat moves 6 km/h in still water. It travels 30 km upriver and 30 km downriver in total time of 18 hrs. What is the speed of the current?\r<BR>\n" );
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document.write( "6 km/h in still water<BR>\n" );
document.write( "30 km upriver (against the current)<BR>\n" );
document.write( "30 km downriver (with the current)<BR>\n" );
document.write( "total time 18 hrs\r<BR>\n" );
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document.write( "let x = speed of boat = 6 km/h<BR>\n" );
document.write( "let y = speed of the current<BR>\n" );
document.write( "let x + y = speed of boat plus the speed of the current (downriver)<BR>\n" );
document.write( "(current speeds up boat)<BR>\n" );
document.write( "x + y = 6 + y<BR>\n" );
document.write( "let x - y = speed of boat minus the speed of the current (upriver)<BR>\n" );
document.write( "(current slows down boat)<BR>\n" );
document.write( "x - y = 6 - y<BR>\n" );
document.write( "D distance = R rate * T time<BR>\n" );
document.write( "30 = (6 + y)T = 6T + yT --> T = 30/(6 + y)<BR>\n" );
document.write( "30 = (6 - y)(18 - T) = 108 - 6T - 18y + yT (used FOIL)<BR>\n" );
document.write( "6T + yT = 108 - 6T - 18y + yT<BR>\n" );
document.write( "6T = 108 - 6T - 18y<BR>\n" );
document.write( "12T = 108 - 18y<BR>\n" );
document.write( "12T + 18y = 108<BR>\n" );
document.write( "12 * 30/(6 + y) + 18y = 108<BR>\n" );
document.write( "12 * 30 + 18y(6 + y) = 108(6 + y)<BR>\n" );
document.write( "360 + 108y + 18y^2 = 648 + 108y<BR>\n" );
document.write( "360 + 18y^2 = 648<BR>\n" );
document.write( "18y^2 = 288<BR>\n" );
document.write( "y^2 = 16<BR>\n" );
document.write( "y = 4 km/h = speed of the current<BR>\n" );
document.write( "D distance = R rate * T time<BR>\n" );
document.write( "downriver --> 30 = (6 + y)T<BR>\n" );
document.write( "30 = (6 + 4)T<BR>\n" );
document.write( "30 = 10T<BR>\n" );
document.write( "3 = T<BR>\n" );
document.write( "upriver --> 30 = (6 - y)(18 - T)<BR>\n" );
document.write( "30 = (6 - 4)(18 - 3)<BR>\n" );
document.write( "30 = 2 * 15<BR>\n" );
document.write( "30 = 30<BR>\n" );
document.write( "so speed of current is 4km/h, they took 3 hours to go downriver and 15 hours to go upriver<BR>\n" );
document.write( " </SPAN>\n" );
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