document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171646>Question 171646</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method Book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Tim paddled his kayak 12 km upstream against a 3 km/h current and back again in 5 h 20 min. In that time how far could he have paddled 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 #126819 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tim paddled his kayak 12 km upstream against a 3 km/h current and back again<BR>\n" );
document.write( " in 5 h 20 min. In that time how far could he have paddled in still water?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = his speed in still water<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-3) = his speed upstream<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(s+3) = his speed downstream<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Write a time equation: time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=distance%2Fspeed ALIGN=MIDDLE  ALT=\"distance%2Fspeed\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 5 hr 20 min to hrs: 5<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Time upstream + time downstream = 5<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s-3%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s%2B3%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply equation by 3(s-3)(s+3)<BR>\n" );
document.write( "3(s-3)(s+3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s-3%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 3(s-3)(s+3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s%2B3%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3(s-3)(s+3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Results:<BR>\n" );
document.write( "36(s+3) + 36(s-3) = 16(s-3)(s+3)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "36s + 108 + 36s - 108 = 16(s^2 - 9)<BR>\n" );
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document.write( "72s = 16s^2 - 144<BR>\n" );
document.write( "Arrange as a quadratic equation:<BR>\n" );
document.write( "16s^2 - 72s - 144 = 0<BR>\n" );
document.write( "Simplify divide equation by 8<BR>\n" );
document.write( "2s^2 - 9s - 18 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(2s + 3)(s - 6) = 0<BR>\n" );
document.write( "Positive solution: <BR>\n" );
document.write( "s = 6 mph; his still water speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "How far would he travel in 5<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs at 6 mph?<BR>\n" );
document.write( "6 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F3 ALIGN=MIDDLE  ALT=\"16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 32 miles<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by find the times<BR>\n" );
document.write( "12/9 = 1.33<BR>\n" );
document.write( "12/3 = 4.0<BR>\n" );
document.write( "Total= 5.33 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );