document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082937>Question 1082937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two botas starts at the same point. One sail due east starting 10 A.M. at a constant rate of 20 kph. The other sail due south starting 11 A.M. at constant rate of 9 kph. How fast are they separating at noon?<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 #701297 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between them is the hypotenuse of a right triangle who's legs are measured by the rate of each boat.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2%2BB%5E2=H%5E2 ALIGN=MIDDLE  ALT=\"A%5E2%2BB%5E2=H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's measure time starting at 11 AM,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=20t%2B20=20%28t%2B1%29 ALIGN=MIDDLE  ALT=\"A=20t%2B20=20%28t%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9t ALIGN=MIDDLE  ALT=\"B=9t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%28t%2B1%29%5E2%2B%289t%29%5E2=H%5E2 ALIGN=MIDDLE  ALT=\"400%28t%2B1%29%5E2%2B%289t%29%5E2=H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%28t%5E2%2B2t%2B1%29%2B81t%5E2=H%5E2 ALIGN=MIDDLE  ALT=\"400%28t%5E2%2B2t%2B1%29%2B81t%5E2=H%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=481t%5E2%2B800t%2B400 ALIGN=MIDDLE  ALT=\"H%5E2=481t%5E2%2B800t%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So at noon, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2 ALIGN=MIDDLE  ALT=\"t=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=481%284%29%2B800%282%29%2B400 ALIGN=MIDDLE  ALT=\"H%5E2=481%284%29%2B800%282%29%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=1924%2B1600%2B400 ALIGN=MIDDLE  ALT=\"H%5E2=1924%2B1600%2B400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=3924 ALIGN=MIDDLE  ALT=\"H%5E2=3924\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=sqrt%283924%29 ALIGN=MIDDLE  ALT=\"H=sqrt%283924%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=6sqrt%28109%29 ALIGN=MIDDLE  ALT=\"H=6sqrt%28109%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now to find the rate of separation, implicitly differentiate the equation above with respect to time.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%28dA%2Fdt%29%2B2B%28dB%2Fdt%29=2H%28dH%2Fdt%29 ALIGN=MIDDLE  ALT=\"2A%28dA%2Fdt%29%2B2B%28dB%2Fdt%29=2H%28dH%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=20%282%2B1%29=60 ALIGN=MIDDLE  ALT=\"A=20%282%2B1%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9%282%29=18 ALIGN=MIDDLE  ALT=\"B=9%282%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdt=20 ALIGN=MIDDLE  ALT=\"dA%2Fdt=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB%2Fdt=9 ALIGN=MIDDLE  ALT=\"dB%2Fdt=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2860%29%2820%29%2B2%2818%29%289%29=2%286sqrt%28109%29%29%28dH%2Fdt%29 ALIGN=MIDDLE  ALT=\"2%2860%29%2820%29%2B2%2818%29%289%29=2%286sqrt%28109%29%29%28dH%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12sqrt%28109%29%28dH%2Fdt%29=2724%29 ALIGN=MIDDLE  ALT=\"12sqrt%28109%29%28dH%2Fdt%29=2724%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dH%2Fdt=227%2Fsqrt%28109%29 ALIGN=MIDDLE  ALT=\"dH%2Fdt=227%2Fsqrt%28109%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28dH%2Fdt=%28227%2F109%29sqrt%28109%29%29 ALIGN=MIDDLE  ALT=\"highlight%28dH%2Fdt=%28227%2F109%29sqrt%28109%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kph ALIGN=MIDDLE  ALT=\"kph\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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