document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=593418>Question 593418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are in a boat a miles from the nearest point on the coast (see figure). You are to go to a point Q, which is b miles down the coast and 1 mile inland. You can row at 4 miles per hour and walk at 5 miles per hour. If a = 2, and b = 4, toward what point on the coast should you row in order to reach Q in the least time? (Round your answer to three decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376433 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=376433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rewrite the problem:<BR>\n" );
document.write( "You are in a boat 2 miles from the nearest point on the coast (see figure, it would be nice!). <BR>\n" );
document.write( "You are to go to a point Q, which is 4 miles down the coast and 1 mile inland.<BR>\n" );
document.write( " You can row at 4 miles per hour and walk at 5 miles per hour. <BR>\n" );
document.write( "Toward what point on the coast should you row in order to reach Q in the least time?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = distance from the coastal point nearest the boat, to where he should land the boat<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(4-x) = distance from the landing point to the coastal point nearest Q<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The distance rowed and and walked will be the hypotenuse of two triangles<BR>\n" );
document.write( "write a time equation; time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "total time = rowing time + walking time<BR>\n" );
document.write( "t(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%5E2%2Bx%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28sqrt%282%5E2%2Bx%5E2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281%5E2%2B%284-x%29%5E2%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%281%5E2%2B%284-x%29%5E2%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%284%2Bx%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28sqrt%284%2Bx%5E2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281%2B%2816-8x%2Bx%5E2%29%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%281%2B%2816-8x%2Bx%5E2%29%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%284%2Bx%5E2%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28sqrt%284%2Bx%5E2%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x%5E2-8x%2B17%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28sqrt%28x%5E2-8x%2B17%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "t(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%28sqrt%284%2Bx%5E2%29%29+%2B+4%28sqrt%28x%5E2-8x%2B17%29%29%29%2F20 ALIGN=MIDDLE  ALT=\"%285%28sqrt%284%2Bx%5E2%29%29+%2B+4%28sqrt%28x%5E2-8x%2B17%29%29%29%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The graph, time on the y axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+10%2C+-2%2C+4%2C%285%28sqrt%284%2Bx%5E2%29%29+%2B+4%28sqrt%28x%5E2-8x%2B17%29%29%29%2F20+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Minimum time, landing point: x = 2 mi from the coastal point nearest the boat,<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sorry I sent this prematurely by mistake.  C </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );