document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170853>Question 170853</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618503080/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.\r<BR>\n" );
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document.write( "word problem for quadratic equations </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126138 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=126138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s=speed of stream\r<BR>\n" );
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document.write( "Remember, the distance-rate-time formula is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   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=d%2Fr=t ALIGN=MIDDLE  ALT=\"d%2Fr=t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by r to solve for t.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation.\r<BR>\n" );
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document.write( "So when she goes upstream (against the current), the stream is slowing her down. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=9-s ALIGN=MIDDLE  ALT=\"r=9-s\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=12 ALIGN=MIDDLE  ALT=\"d=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the equation for the upstream portion of the journey is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12%2F%289-s%29 ALIGN=MIDDLE  ALT=\"t=12%2F%289-s%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "When she goes downstream (with the current), the stream is speeding her up. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=9%2Bs ALIGN=MIDDLE  ALT=\"r=9%2Bs\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=12 ALIGN=MIDDLE  ALT=\"d=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the equation for the downstream portion of the journey is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=12%2F%289%2Bs%29 ALIGN=MIDDLE  ALT=\"t=12%2F%289%2Bs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now simply add these two equations together to get the total time 3 hours like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%289-s%29%2B12%2F%289%2Bs%29=3 ALIGN=MIDDLE  ALT=\"12%2F%289-s%29%2B12%2F%289%2Bs%29=3\"   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=12%289%2Bs%29%2B12%289-s%29=3%289-s%29%289%2Bs%29 ALIGN=MIDDLE  ALT=\"12%289%2Bs%29%2B12%289-s%29=3%289-s%29%289%2Bs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-s%29%289%2Bs%29 ALIGN=MIDDLE  ALT=\"%289-s%29%289%2Bs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%289%2Bs%29%2B12%289-s%29=3%2881-s%5E2%29 ALIGN=MIDDLE  ALT=\"12%289%2Bs%29%2B12%289-s%29=3%2881-s%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2B12s%2B108-12s=243-3s%5E2 ALIGN=MIDDLE  ALT=\"108%2B12s%2B108-12s=243-3s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=216=243-3s%5E2 ALIGN=MIDDLE  ALT=\"216=243-3s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27=-3s%5E2 ALIGN=MIDDLE  ALT=\"-27=-3s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 243 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=s%5E2 ALIGN=MIDDLE  ALT=\"9=s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   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=s=3 ALIGN=MIDDLE  ALT=\"s=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides. Note: only the positive square root is considered. \r<BR>\n" );
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document.write( "So the speed of the stream is 3 km/hr\r<BR>\n" );
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