document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=826008>Question 826008</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ship A was sailing due to South at the rate of 6 miles per hour and another ship B was sailing due to East at the rate of 8 miles per hour. At 4 PM ship B crossed the position where hip A was 2 hours before.<BR>\n" );
document.write( "1) At what rate were they approaching or separating at 3 PM ?<BR>\n" );
document.write( "2) At what rate were they changing the distance between them at 5 PM ?<BR>\n" );
document.write( "3) When was the distance between them not changing ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497784 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ship A was sailing due to South at the rate of 6 miles per hour and another ship B was sailing due to East at the rate of 8 miles per hour. At 4 PM ship B crossed the position where hip A was 2 hours before.<BR>\n" );
document.write( "Use 2 PM as the starting point.<BR>\n" );
document.write( "Ship A is 12 miles North of it, and ship B is at the point.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Find the distance between the ships as a function of time (in hours).<BR>\n" );
document.write( "t = 0 at the starting point.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Ship A's distance from the SP is 12 - 6t miles<BR>\n" );
document.write( "Ship B's distance from the SP is 8t miles<BR>\n" );
document.write( "The distance between them is the hypotenuse of a right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+=+%2812-6t%29%5E2+%2B+%288t%29%5E2+=+100t%5E2+-+144t+%2B+144 ALIGN=MIDDLE  ALT=\"s%5E2+=+%2812-6t%29%5E2+%2B+%288t%29%5E2+=+100t%5E2+-+144t+%2B+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+sqrt%28100t%5E2+-+144t+%2B+144%29 ALIGN=MIDDLE  ALT=\"s+=+sqrt%28100t%5E2+-+144t+%2B+144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the relative speed, ds/dt<BR>\n" );
document.write( "ds/dt = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2Fsqrt%28100t%5E2+-+144t+%2B+144%29%2A%28200t+-+144%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2Fsqrt%28100t%5E2+-+144t+%2B+144%29%2A%28200t+-+144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s'(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100t-72%29%2Fsqrt%28100t%5E2+-+144t+%2B+144%29 ALIGN=MIDDLE  ALT=\"%28100t-72%29%2Fsqrt%28100t%5E2+-+144t+%2B+144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s'(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850t-36%29%2Fsqrt%2825t%5E2+-+36t+%2B+36%29 ALIGN=MIDDLE  ALT=\"%2850t-36%29%2Fsqrt%2825t%5E2+-+36t+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "1) At what rate were they approaching or separating at 3 PM ?<BR>\n" );
document.write( "3 PM is t = 1<BR>\n" );
document.write( "s'(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850-36%29%2Fsqrt%2825+-+36+%2B+36%29 ALIGN=MIDDLE  ALT=\"%2850-36%29%2Fsqrt%2825+-+36+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 14/5 = 2.8 mi/hr<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "2) At what rate were they changing the distance between them at 5 PM ?<BR>\n" );
document.write( "5 PM --> t = 3<BR>\n" );
document.write( "s'(3) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%2A3-36%29%2Fsqrt%2825%2A9+-+36%2A3+%2B+36%29 ALIGN=MIDDLE  ALT=\"%2850%2A3-36%29%2Fsqrt%2825%2A9+-+36%2A3+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=114%2Fsqrt%28153%29 ALIGN=MIDDLE  ALT=\"114%2Fsqrt%28153%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38%2Fsqrt%2817%29 ALIGN=MIDDLE  ALT=\"38%2Fsqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=~ 9.216 mi/hr<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "3) When was the distance between them not changing ?<BR>\n" );
document.write( "s'(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850t-36%29%2Fsqrt%2825t%5E2+-+36t+%2B+36%29 ALIGN=MIDDLE  ALT=\"%2850t-36%29%2Fsqrt%2825t%5E2+-+36t+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "50t-36 = 0<BR>\n" );
document.write( "t = 0.72 hrs past 2 PM<BR>\n" );
document.write( "t = 2:43:12 PM<BR>\n" );
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document.write( "The speeds in parts 1 & 2 are both separating, since they're past the time in part 3.<BR>\n" );
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document.write( "It appears to be a simple problem, but is complex.  At least it's a right triangle. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );