document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5684>Question 5684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this and keep thinking in circles.  I would really appreciate your help.  Here is the question that we are to use quadratic equations to solve.\r<BR>\n" );
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document.write( "She rows 12km upstream and 12 km downstream in 3hrs.  The speed of her boat in still water is 9km/hr.  find the speed of the stream.\r<BR>\n" );
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document.write( "This is what I have come up with so far.  r= d/t\r<BR>\n" );
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document.write( "Upstream<BR>\n" );
document.write( "d=12 <BR>\n" );
document.write( "r= x-9<BR>\n" );
document.write( "t= \r<BR>\n" );
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document.write( "Downstream<BR>\n" );
document.write( "d=12<BR>\n" );
document.write( "r= x+9<BR>\n" );
document.write( "t=\r<BR>\n" );
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document.write( "I'm not sure how to put all the information together to solve.  I tried\r<BR>\n" );
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document.write( "12/(x-9) + 12/(x+9)= 3<BR>\n" );
document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2927 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your answer looks fine actually, well done. However, being a mathematician, I have my own tried and tested method, shown here.\r<BR>\n" );
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document.write( "As you say, speed = distance/time.\r<BR>\n" );
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document.write( "Let x=speed of the boat in still water.<BR>\n" );
document.write( "Let t = time taken to travel upstream\r<BR>\n" );
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document.write( "<b>Upstream</b>:<BR>\n" );
document.write( "speed = x-9<BR>\n" );
document.write( "distance = 12<BR>\n" );
document.write( "time = t\r<BR>\n" );
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document.write( "<b>Downstream</b>:<BR>\n" );
document.write( "speed = x+9<BR>\n" );
document.write( "distance = 12<BR>\n" );
document.write( "time = 3-t\r<BR>\n" );
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document.write( "so, upstream, we get x-9 = 12/t and downstream, we get x+9 = 12/(3-t).\r<BR>\n" );
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document.write( "so, re-arrange for t, since we are not interested in that, and we wish to get rid of it:\r<BR>\n" );
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document.write( "t = 12/(x-9) and 3-t = 12/(x+9) --> t = 3 - 12/(x+9).\r<BR>\n" );
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document.write( "Equating these 2 gives us 12/(x-9) = 3 - 12/(x+9), which is 12/(x-9) + 12/(x+9) = 3 --> your equation :-).\r<BR>\n" );
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document.write( "So, multiply every term by (x+9)(x-9) -->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%28x%2B9%29%28x-9%29%29%2F%28x-9%29+%2B+%2812%28x%2B9%29%28x-9%29%29%2F%28x%2B9%29+=+3%28x%2B9%29%28x-9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. we can cancel some terms on the left hand side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28x%2B9%29+%2B+12%28x-9%29+=+3%28x%2B9%29%28x-9%29 ALIGN=MIDDLE  ALT=\"12%28x%2B9%29+%2B+12%28x-9%29+=+3%28x%2B9%29%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> divide everything by 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B9%29+%2B+4%28x-9%29+=+%28x%2B9%29%28x-9%29 ALIGN=MIDDLE  ALT=\"4%28x%2B9%29+%2B+4%28x-9%29+=+%28x%2B9%29%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B36+%2B+4x-36+=+%28x%5E2-81%29 ALIGN=MIDDLE  ALT=\"4x%2B36+%2B+4x-36+=+%28x%5E2-81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+=+x%5E2+-+81 ALIGN=MIDDLE  ALT=\"8x+=+x%5E2+-+81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+8x+-+81+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+8x+-+81+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, factorise (not sure it does easily) or plug into the quadratic formula. I shall leave this for you to do. Good luck. Oh yes, check my working because i am not happy that the equation doesn't factorise...perhaps the answer is a nive fraction...work it out :-)\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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