document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100776>Question 1100776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with this? Thank you. <BR>\n" );
document.write( "A man can row his boat at a rate of 4 mph and he can run at a rate of 7 mph. He is 1 mile directly west of a point on an north-south shoreline, and the camp he needs to reach is 2 miles south of that same point on the shoreline. <BR>\n" );
document.write( "1. How far down the shoreline should he row to minimize the amount of time it will take him to get to the camp? <BR>\n" );
document.write( "2. What is the minimum time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715342 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Helps to draw this\r<BR>\n" );
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document.write( "If he rows directly to the site, the distance is sqrt (1+4)=sqrt(5) miles<BR>\n" );
document.write( "At 4 mph, that is 33.5 minutes or .559 hours<BR>\n" );
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document.write( "If he rows directly to shore, the distance is 1 mile and the time 1/4 hr 15 min.  He then runs down the shore 2 miles at 7 miles per hour, and that is 2/7 of an hour or 120/7 min or 17.1 min.  The total time is 32.1 min.<BR>\n" );
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document.write( "The distance rowed is sqrt (1+x^2), where x is the distance south of the point. The time is sqrt (1+x^2)/4 hours.<BR>\n" );
document.write( "The distance down the shore line is 2-x miles, and the time is (2-x)/7 hours<BR>\n" );
document.write( "Take the first derivative of the sum<BR>\n" );
document.write( "(1/4)*(1/2)(2x)(1/sqrt(1+x^2))-(1/7)=0<BR>\n" );
document.write( "This is x/4sqrt(1+x^2)-(1/7)=0<BR>\n" );
document.write( "so (1/7)=x/4sqrt(1+x^2)<BR>\n" );
document.write( "4sqrt(1+x^2)=7x<BR>\n" );
document.write( "16(x^2+1)=49x^2<BR>\n" );
document.write( "16x^2+16=49x^2<BR>\n" );
document.write( "33x^2=16<BR>\n" );
document.write( "x=0.696 miles\r<BR>\n" );
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document.write( "distance rowed is sqrt(1+0.485^2)=1.22 miles, and that takes .3046 hours or 18.28 min<BR>\n" );
document.write( "The distance run is 1.304 miles, and that takes 0.186 hours or 11.18 minutes<BR>\n" );
document.write( "Total time is 29.46 minutes<BR>\n" );
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