document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249957>Question 249957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat can travel 9mph in still water. It travels 7 miles downstream in the same time that it travels only 3 miles upstream. Find 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 #181967 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=181967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by setting up the variables you will need.<BR>\n" );
document.write( "s = speed in still water = 9 mph<BR>\n" );
document.write( "c = current<BR>\n" );
document.write( "d = rt is the basic distance formula, where d=distance, r=rate, and t=time<BR>\n" );
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document.write( "Now translate the English into math.<BR>\n" );
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document.write( "Traveling downstream:<BR>\n" );
document.write( "r = s+c     The current adds to the boat's speed.<BR>\n" );
document.write( "d=7 in time t<BR>\n" );
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document.write( "Traveling upstream:<BR>\n" );
document.write( "r = s - c    The current subtracts from the boat's speed.<BR>\n" );
document.write( "d =3 in time t<BR>\n" );
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document.write( "We are told t=t so we can rearrange both equation to define 't'.<BR>\n" );
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document.write( "7 = (s+c) * t<BR>\n" );
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document.write( "Divide both sides by (s+c)<BR>\n" );
document.write( "7/(s+c) = t<BR>\n" );
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document.write( "The other equation is:<BR>\n" );
document.write( "3 = (s-c) * t<BR>\n" );
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document.write( "Divide both sides by (s-c)<BR>\n" );
document.write( "3/(s-c) = t<BR>\n" );
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document.write( "Since both equations = t, we can use this fact to set them equal to one another<BR>\n" );
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document.write( "7/(s+c) = 3/(s-c)<BR>\n" );
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document.write( "Cross multiply<BR>\n" );
document.write( "7(s-c) = 3(s+c)<BR>\n" );
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document.write( "7s - 7c = 3s + 3c<BR>\n" );
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document.write( "4s = 10c<BR>\n" );
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document.write( "Recall s = 9<BR>\n" );
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document.write( "4(9) = 36 = 10c<BR>\n" );
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document.write( "c = 3.6<BR>\n" );
document.write( "The current runs at 3.6 mph<BR>\n" );
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document.write( "Next substitute back into the original equations to see if this answer is correct.<BR>\n" );
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document.write( "How long does it take to go 7 miles downstream?<BR>\n" );
document.write( "7 = (9+3.6)t = 12.6t<BR>\n" );
document.write( "t = 7/12.6 = .555555556<BR>\n" );
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document.write( "3 = (9-3.6)t = 5.4t<BR>\n" );
document.write( "t = 3/5.4 = .555555556<BR>\n" );
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document.write( "So we can conclude the current of the river is 3.6 mph.<BR>\n" );
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document.write( "Done </SPAN>\n" );
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