document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009854>Question 1009854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify the variables, write a system of equations to solve<BR>\n" );
document.write( "(Problem on my exam study guide)<BR>\n" );
document.write( "When she rows with the current, Mindy can row 24 miles in 3 hours. Against the same current, Mindy can row only &#8532; of this distance in 4 hours. Find the rate of the current and Mindy's rowing rate in still water. Assume that both are constant. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625337 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=625337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance<BR>\n" );
document.write( "let a = the rate of the boat<BR>\n" );
document.write( "let b = the rate of the current.\r<BR>\n" );
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document.write( "with the current, the rates are additive.<BR>\n" );
document.write( "against the current, the rate are subtactive.\r<BR>\n" );
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document.write( "going with the current, rate * time becomes:\r<BR>\n" );
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document.write( "(a + b) * 3 = 24\r<BR>\n" );
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document.write( "going agains the current, rate * time becomes:\r<BR>\n" );
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document.write( "(a - b) * 4 = 16\r<BR>\n" );
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document.write( "simplify these equations to get:\r<BR>\n" );
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document.write( "3a + 3b = 24<BR>\n" );
document.write( "4a - 4b = 16\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 4 and multiply the second equation by 3 to get:\r<BR>\n" );
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document.write( "12a + 12b = 96<BR>\n" );
document.write( "12a - 12b = 48\r<BR>\n" );
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document.write( "add the equations together to get:\r<BR>\n" );
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document.write( "24a = 144\r<BR>\n" );
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document.write( "solve for a to get a = 6\r<BR>\n" );
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document.write( "your original equations are:\r<BR>\n" );
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document.write( "(a + b) * 3 = 24<BR>\n" );
document.write( "(a - b) * 4 = 16\r<BR>\n" );
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document.write( "replace a in the first equation to get:\r<BR>\n" );
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document.write( "(6 + b) * 3 = 24<BR>\n" );
document.write( "distribute the multiplication to get:<BR>\n" );
document.write( "18 + 3b = 24<BR>\n" );
document.write( "subtract 18 from both sides to get:<BR>\n" );
document.write( "3b = 6<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 2\r<BR>\n" );
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document.write( "you have a = 6 and b = 2<BR>\n" );
document.write( "this means the rate of the boat is 6 mph and the rate of the current is 2 mph.\r<BR>\n" );
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document.write( "go back to your original equations again and replace a with 6 and b with 2 to get:\r<BR>\n" );
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document.write( "(a + b) * 3 = 24 becomes (6+2) * 3 = 24 which becomes 8*3 = 24 which becomes 24 = 24.\r<BR>\n" );
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document.write( "(a - b) * 4 = 16 becomes (6-2) * 4 = 16 which becomes 4 * 4 = 16 which becomes 16 = 16.\r<BR>\n" );
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document.write( "this confirms the solutions are correct.\r<BR>\n" );
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document.write( "the rate of the boat is 6 miles per hour.<BR>\n" );
document.write( "the rate of the current is 2 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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