document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248519>Question 248519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me help my son with this word problem ...\r<BR>\n" );
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document.write( "A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water? What is the rate 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 #181125 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=181125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We start with what we know about distance problems.<BR>\n" );
document.write( "d = r * t, where d=distance, r=rate, and t=time<BR>\n" );
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document.write( "Upstream info:<BR>\n" );
document.write( "60=r*5<BR>\n" );
document.write( "r = 12 mph<BR>\n" );
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document.write( "Downstream<BR>\n" );
document.write( "60 = r*3<BR>\n" );
document.write( "r = 20<BR>\n" );
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document.write( "We need to assume the boat runs as fast as possible in both directions, otherwise we cannot solve the problem.<BR>\n" );
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document.write( "Let's call the upstream rate:  U<BR>\n" );
document.write( "Let's call the downstream rate:  D<BR>\n" );
document.write( "Let's call the unknown maximum rate:  X<BR>\n" );
document.write( "And finally, the current is flowing at C mph.<BR>\n" );
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document.write( "Upstream:<BR>\n" );
document.write( "U = X-C<BR>\n" );
document.write( "In English, the upstream rate = max speed of the boat MINUS the current flowing against it.;<BR>\n" );
document.write( "X - C = 12, as shown above.<BR>\n" );
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document.write( "Downstream:<BR>\n" );
document.write( "D = X + C<BR>\n" );
document.write( "In English, the downstream rate = max speed of the boat PLUS the current pushing it along.<BR>\n" );
document.write( "X+C=20<BR>\n" );
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document.write( "So we have two equations and two unknowns. Piece of cake.  Right?<BR>\n" );
document.write( "X - C = 12<BR>\n" );
document.write( "X + C = 20<BR>\n" );
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document.write( "Let's add them.<BR>\n" );
document.write( "2X = 32<BR>\n" );
document.write( "X = 16<BR>\n" );
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document.write( "So the unknown maximum speed X is 16.<BR>\n" );
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document.write( "Now we check our work, as we always do...<BR>\n" );
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document.write( "Looking back at what we know,<BR>\n" );
document.write( "X-C = 12<BR>\n" );
document.write( "16-C=12<BR>\n" );
document.write( "C=4<BR>\n" );
document.write( "OK<BR>\n" );
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document.write( "And we know<BR>\n" );
document.write( "X+C = 20<BR>\n" );
document.write( "16 + C = 20<BR>\n" );
document.write( "C=4<BR>\n" );
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document.write( "Checking the upstream rate...<BR>\n" );
document.write( "60/(16-4)= 60/12  = 5, which is how long we were told it took.<BR>\n" );
document.write( "Checking the downstream rate...<BR>\n" );
document.write( "60/(16+4) = 60/20 = 3, which is how long we were told it took.<BR>\n" );
document.write( "Done. </SPAN>\n" );
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