document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146100>Question 1146100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat traveled 260 miles downstream and back. The trip downstream took 13 hours. he trip back took 26 hours. Find the speed of the boat in still water and the speed 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 #767382 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r * t = d<BR>\n" );
document.write( "r = rate<BR>\n" );
document.write( "t = time<BR>\n" );
document.write( "d = distance\r<BR>\n" );
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document.write( "b = the rate of the boat<BR>\n" );
document.write( "c = the rate of the current\r<BR>\n" );
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document.write( "going with the current, r = b + c<BR>\n" );
document.write( "going against the current, r = b - c\r<BR>\n" );
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document.write( "your formulas become:\r<BR>\n" );
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document.write( "with the current:<BR>\n" );
document.write( "(b + c) * t = d\r<BR>\n" );
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document.write( "against the current:<BR>\n" );
document.write( "(b - c) * t = d\r<BR>\n" );
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document.write( "d - 259 nukes<BR>\n" );
document.write( "t = 13 hours going with the current.<BR>\n" );
document.write( "t = 26 hours going against the current.\r<BR>\n" );
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document.write( "your formulas become:\r<BR>\n" );
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document.write( "with the current:<BR>\n" );
document.write( "(b + c) * 13 = 260\r<BR>\n" );
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document.write( "against the current:<BR>\n" );
document.write( "(b - c) * 26 = 260\r<BR>\n" );
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document.write( "simplify both formulas to get:<BR>\n" );
document.write( "13b + 13c = 260<BR>\n" );
document.write( "26b - 26c = 260\r<BR>\n" );
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document.write( "these two equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:<BR>\n" );
document.write( "26b + 26c = 520<BR>\n" );
document.write( "26b - 26c = 260\r<BR>\n" );
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document.write( "add both equations together to get:<BR>\n" );
document.write( "52b = 780\r<BR>\n" );
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document.write( "solve for b to get:<BR>\n" );
document.write( "b = 780/52 = 15\r<BR>\n" );
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document.write( "in the first of the two equations, replace b with 15 and solve for c.<BR>\n" );
document.write( "start with 13b + 13c = 260<BR>\n" );
document.write( "replace b with 15 to get 13*15 + 13c = 260<BR>\n" );
document.write( "simplify to get 195 + 13c = 260<BR>\n" );
document.write( "subtract 195 from both sides to get:<BR>\n" );
document.write( "13c = 65<BR>\n" );
document.write( "solve for c to get c = 65/13 = 5\r<BR>\n" );
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document.write( "replace b with 15 and c with 5 in both original equations to get:<BR>\n" );
document.write( "13b + 13c = 13*15 + 13*5 = 195 + 65 = 260<BR>\n" );
document.write( "26b - 26c = 26*15 - 26*5 = 390 - 130 = 260\r<BR>\n" );
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document.write( "b = 15 and c = 5 are confirmed to be good values.<BR>\n" );
document.write( "your solution is that the rate of the boat is 15 miles per hour and the rate of the current is 5 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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