document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636835>Question 636835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A river boat's speed is 5 kilometers/hour on standing water when it is charged and 15 kilometers an hour on standing water when it is empty. The boat sets sail charged up the river (against the current) to a distance of 81 kilometers. It returns (against the current) empty. The total sailing time there and back, including 3 hours of docking for unloading the cargo, is 48 hours. What is the speed of the current?\r<BR>\n" );
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document.write( "I have no clue how to do this problem, and never did a problem like this before. Thanks for all the help, I really appreciate it! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401253 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=401253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A river boat's speed is 5 kilometers/hour on standing water when it is charged<BR>\n" );
document.write( " and 15 kilometers an hour on standing water when it is empty.<BR>\n" );
document.write( " The boat sets sail charged up the river (against the current) to a distance<BR>\n" );
document.write( " of 81 kilometers.<BR>\n" );
document.write( " It returns (against the current) empty.<BR>\n" );
document.write( " The total sailing time there and back, including 3 hours of docking for <BR>\n" );
document.write( "unloading the cargo, is 48 hours. <BR>\n" );
document.write( "What is the speed of the current?<BR>\n" );
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document.write( "The way this reads, it is against the current up and back, but that doesn't<BR>\n" );
document.write( " make sense. Assume it returns with the current<BR>\n" );
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document.write( "Let c = rate of the current<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(5-c) = effective speed upstream, charged<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(15+c) = effective speed downstream, empty<BR>\n" );
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document.write( "From the information given, we know the sailing time is 45 hrs (3hrs to unload)<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 = 45 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F%285-c%29 ALIGN=MIDDLE  ALT=\"81%2F%285-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F%2815%2Bc%29 ALIGN=MIDDLE  ALT=\"81%2F%2815%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 45<BR>\n" );
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document.write( "multiply by (5-c)(15+c)*<BR>\n" );
document.write( "(5-c)(15+c)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F%285-c%29 ALIGN=MIDDLE  ALT=\"81%2F%285-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (5-c)(15+c)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2F%2815%2Bc%29 ALIGN=MIDDLE  ALT=\"81%2F%2815%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 45(5-c)(15+c)<BR>\n" );
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document.write( "Cancel out the denominators, results<BR>\n" );
document.write( "81(15+c) + 81(5-c) = 45(75+5c-15c-c^2)<BR>\n" );
document.write( "1215 + 81c + 405 - 81c = 45(75-10c-c^2)<BR>\n" );
document.write( "1620 = 3375 - 450c - 45c^2<BR>\n" );
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document.write( "combine like terms on the left<BR>\n" );
document.write( "45c^2 + 450c - 3375 + 1620 = 0<BR>\n" );
document.write( "45c^2 + 450c - 1755 = 0<BR>\n" );
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document.write( "Simplify, divide by 45, results<BR>\n" );
document.write( "c^2 + 10c - 39 = 0<BR>\n" );
document.write( "Factors to <BR>\n" );
document.write( "(c+13)(c-3) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "c = 3 km/h is the current<BR>\n" );
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document.write( "Check the solution find the time each way<BR>\n" );
document.write( "81/(5 - 3) = 40.5 hrs<BR>\n" );
document.write( "81/(15 +3) =  4.5<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "total time: 45 hrs; confirms our solution of current is 3 km/h<BR>\n" );
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document.write( "Did all this make sense to you here?  C </SPAN>\n" );
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