document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020566>Question 1020566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour. The motorboat then returns to the original place heading downstream. The total trip up and back takes 6 hours. What was the speed of the motorboat assuming it maintained a constant speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636452 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=636452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour.<BR>\n" );
document.write( " The motorboat then returns to the original place heading downstream.<BR>\n" );
document.write( " The total trip up and back takes 6 hours.<BR>\n" );
document.write( " What was the speed of the motorboat assuming it maintained a constant speed?<BR>\n" );
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document.write( "let s = the speed of the boat in still water<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-3) = effective speed upstream<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(s+3) = effective speed downstream<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "Time up + time down = 6 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F%28s-3%29 ALIGN=MIDDLE  ALT=\"24%2F%28s-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"24%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6<BR>\n" );
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document.write( "Multiply equation by (s-3)(s+3), cancel the denominators and you have<BR>\n" );
document.write( "24(s+3) + 24(s-3) = 6(s-3)(s+3)<BR>\n" );
document.write( "24s + 72 + 24s - 72 = 6(s^2 - 9)<BR>\n" );
document.write( "48s = 6s^2 - 54<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = 6s^2 - 48s - 54<BR>\n" );
document.write( "Simplify, divide by 6<BR>\n" );
document.write( "s^2 - 8s - 9 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s - 9) (s + 1) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "s = 9 mph the speed of the boat in still water<BR>\n" );
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document.write( "Check this, find the time each way<BR>\n" );
document.write( "24/6 = 4 hrs upstream<BR>\n" );
document.write( "24/12 = 2 hrs down<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "total: 6 hrs<BR>\n" );
document.write( " </SPAN>\n" );
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