document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890509>Question 890509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is as under :<BR>\n" );
document.write( "\" Alight house is located at A, 2 km off-shore from the nearest point O on a straight beach and a shop is located at B. The shop is located on the beach , 4 km distant from O. If the housekeeper can row at the rate of 4 km/hour and walk at the rate of 6 km/hr, where should he plan to reach the shore, so as to cover the distance to the shop in the least possible time ? \"\r<BR>\n" );
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document.write( "The question is related to maxima and minima chapter in differential calculus.\r<BR>\n" );
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document.write( "Please send step by step solution of the above question.\r<BR>\n" );
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document.write( "Regards,\r<BR>\n" );
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document.write( "Khoka123 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539075 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=539075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A light house, a shop, and a housekeeper.  Where does the housekeeper begin?  From the light house?   I could analyze and solve the problem if you make the description understandably precise.\r<BR>\n" );
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document.write( "I believe I have an understanding of the description after thinking through the description.\r<BR>\n" );
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document.write( "Draw a right triangle.  Vertical segment OB, showing B below O, and point A to the right of point O.   Segment OB is 4, and segment OA is 2.  The angle AOB is a right angle.\r<BR>\n" );
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document.write( "The housekeeper will row from the light house (?)  to point P between O and B.  \r<BR>\n" );
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document.write( "Let y = Distance for walking which is segment PB.<BR>\n" );
document.write( "That means 4-y is length of OP.\r<BR>\n" );
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document.write( "Distance Rowing, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28sqrt%282%5E2%2B%284-y%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28sqrt%282%5E2%2B%284-y%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distance Walking, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Uniform Rates usually for travel can be represented RT=D, or T=D/R.<BR>\n" );
document.write( "Using a function for total time, T you have total time for this housekeepers row & walk trip as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28T=sqrt%284%2B%284-y%29%5E2%29%2F4%2By%2F6%29 ALIGN=MIDDLE  ALT=\"highlight_green%28T=sqrt%284%2B%284-y%29%5E2%29%2F4%2By%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Find the derivative, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2Fdy ALIGN=MIDDLE  ALT=\"dT%2Fdy\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In one of its raw forms, this starts as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2Fdy=%281%2F4%29%281%2F2%29%284-%284-y%29%5E2%29%5E%28-1%2F2%29%2A2%284-y%29%28-1%29%2B%281%2F6%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equating that to 0, and then omitting the many algebra steps here,  I am finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2813y%5E2%2B40y%2B192=0%29 ALIGN=MIDDLE  ALT=\"highlight%2813y%5E2%2B40y%2B192=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  if this has a real solution, then I believe I made no mistakes...\r<BR>\n" );
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document.write( "I MADE A MISTAKE IN MY WORK, SOMEWHERE.  MAYBE YOU WILL FIND IT AND GET THE RIGHT ANSWER.\r<BR>\n" );
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document.write( "RETRIED SOLUTION-------------------------------------------------------\r<BR>\n" );
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document.write( "The same formula for T was found.<BR>\n" );
document.write( "Derivative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dT%2Fdy=-%28%284-y%29%2F%28sqrt%284%2B%284-y%29%5E2%29%29%29%2B1%2F6 ALIGN=MIDDLE  ALT=\"dT%2Fdy=-%28%284-y%29%2F%28sqrt%284%2B%284-y%29%5E2%29%29%29%2B1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Simplifying and then focusing on the numerator being 0 gave <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2835y%5E2-280y%2B4=0%29 ALIGN=MIDDLE  ALT=\"highlight%2835y%5E2-280y%2B4=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Two solutions for y were found, and the choice which makes sense was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=0.18%29 ALIGN=MIDDLE  ALT=\"highlight%28y=0.18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The calculations and computation to find that are omitted here, taking nearly a whole page on paper.\r<BR>\n" );
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document.write( "The housekeeper would row to a point between O and B, 0.18 km from the point B (the shop).\r<BR>\n" );
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