document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236320>Question 236320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a motor boat travels 36km down stream in 2 hours . in coming back up streams, the <BR>\n" );
document.write( "trip takes 3 hours. find the rate of the boat in still water and the rate of the current.(solve using linear system)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173987 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=173987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "the rate is a combination of the boat and the stream.\r<BR>\n" );
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document.write( "with the stream, the rate is (b+s)\r<BR>\n" );
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document.write( "against the stream, the rate is (b-s)\r<BR>\n" );
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document.write( "b is the rate of the boat<BR>\n" );
document.write( "s is the rate of the stream.<BR>\n" );
document.write( "h is the time in hours.<BR>\n" );
document.write( "d = distance\r<BR>\n" );
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document.write( "going downstream, the formula for rate * time = distance becomes:\r<BR>\n" );
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document.write( "(b+s) * 2 = 36 (equation 1)\r<BR>\n" );
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document.write( "coming back up stream, the formula for rate * time = distance becomes:\r<BR>\n" );
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document.write( "(b-s) * 3 = 36 (equation 2)\r<BR>\n" );
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document.write( "since both these formulas are equal to 36, then they both must be equal to each other, so we have:\r<BR>\n" );
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document.write( "(b+s) * 2 = (b-s) * 3\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( "2b + 2s = 3b - 3s\r<BR>\n" );
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document.write( "subtract 2b and add 3s to both sides of this equation to get:\r<BR>\n" );
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document.write( "3s + 2s = 3b - 2b which becomes:\r<BR>\n" );
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document.write( "5s = b\r<BR>\n" );
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document.write( "replace b with 5s in equation 1 to get:\r<BR>\n" );
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document.write( "(b+s) * 2 = 36 (equation 1) becomes:\r<BR>\n" );
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document.write( "(5s+s) * 2 = 36 which becomes\r<BR>\n" );
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document.write( "6s * 2 = 36 which becomes:\r<BR>\n" );
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document.write( "12s = 36 which becomes\r<BR>\n" );
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document.write( "s = 3\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "s = 3<BR>\n" );
document.write( "b = 5s = 5*3 = 15\r<BR>\n" );
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document.write( "replace s and b in both original equations to confirm the answers are good for both equations.\r<BR>\n" );
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document.write( "both original equations are:\r<BR>\n" );
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document.write( "(b+s) * 2 = 36 (equation 1)<BR>\n" );
document.write( "(b-s) * 3 = 36 (equation 2)\r<BR>\n" );
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document.write( "replace b with 15 and s with 3 to get:\r<BR>\n" );
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document.write( "(15+3) * 2 = 36 (equation 1)<BR>\n" );
document.write( "(15-3 * 3 = 36 (equation 2)\r<BR>\n" );
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document.write( "these equations bgecome:\r<BR>\n" );
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document.write( "18*2 = 36<BR>\n" );
document.write( "12*3 = 36\r<BR>\n" );
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document.write( "since both equations are true, the answer is confirmed.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "rate of the boat is 15 miles per hour.<BR>\n" );
document.write( "rate of the stream is 3 miles per hour.\r<BR>\n" );
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