document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=545126>Question 545126</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At noon, the cruise ship Celebration is 60 miles due south of the cruise ship Inspiration and is sailing north at a rate of 30 mph. If the inspiration is sailing west at a rate of 20 mph, find the time at which the distance d between the ships is a minimum. What is this distance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #355489 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=355489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At noon, the cruise ship Celebration is 60 miles due south of the cruise ship Inspiration and is sailing north at a rate of 30 mph.<BR>\n" );
document.write( " If the inspiration is sailing west at a rate of 20 mph, find the time at which the distance d between the ships is a minimum.<BR>\n" );
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document.write( "let t = the travel time in hrs of both ships<BR>\n" );
document.write( "then<BR>\n" );
document.write( "30t = travel dist of the Celebration (sailing north toward the ref point)<BR>\n" );
document.write( "20t = travel dist of the Inspiration (sailing west from the ref point)<BR>\n" );
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document.write( "The two ships course form a right triangle from the ref point<BR>\n" );
document.write( "The distance between the two ships, is the hypotenuse (d)<BR>\n" );
document.write( "d^2 = (60-30t)^2 + (20t)^2<BR>\n" );
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document.write( "d^2 = 3600 - 1800t - 1800t + 900t^2 + 400t^2<BR>\n" );
document.write( "d^2 = 3600 - 3600t + 1300t^2<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281300t%5E2+-+3600t+%2B+3600%29 ALIGN=MIDDLE  ALT=\"sqrt%281300t%5E2+-+3600t+%2B+3600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can ignore the square root when we find the axis of symmetry<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-3600%29%2F%282%2A1300%29 ALIGN=MIDDLE  ALT=\"-%28-3600%29%2F%282%2A1300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3600%2F2600 ALIGN=MIDDLE  ALT=\"3600%2F2600\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F13 ALIGN=MIDDLE  ALT=\"18%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 1.3846 hrs the distance between them will be minimum<BR>\n" );
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document.write( "What is this distance?<BR>\n" );
document.write( "Find the distance each ship is from the ref point in 1.3846 hrs<BR>\n" );
document.write( "60-(30*1.3846) = 18.46, northbound Celebration<BR>\n" );
document.write( "1.3846*20 = 27.7, westbound Inspiration<BR>\n" );
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document.write( "Find the distance between the ships at this time<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818.46%5E2+%2B+27.7%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2818.46%5E2+%2B+27.7%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 33.3 mi apart at this time\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );