document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=578988>Question 578988</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man is on a lake in a canoe one kilometer from the closest point P of a straight shore line. He wishes to get to his campsite at point Q, 10 kilometers along the shore form point P. In order to accomplish this, he paddles to point R between P and Q then walks the remaining distance to Q. He can paddle 3 km/hr and walk 5 km/hr. How should he pick the ponit R so as to get to Q as quickly possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370899 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=370899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man is on a lake in a canoe one kilometer from the closest point P of a straight shore line.<BR>\n" );
document.write( " He wishes to get to his campsite at point Q, 10 kilometers along the shore form point P.<BR>\n" );
document.write( " In order to accomplish this, he paddles to point R between P and Q then walks the remaining distance to Q.<BR>\n" );
document.write( " He can paddle 3 km/hr and walk 5 km/hr.<BR>\n" );
document.write( "How should he pick the ponit R so as to get to Q as quickly possible?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let r = the distance from point p <BR>\n" );
document.write( "the distance he paddles will be the hypotenuse of a triangle formed by 1 kr and r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%5E2%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%281%5E2%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the time if he paddles at 3 km/h<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281%5E2%2Br%5E2%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28sqrt%281%5E2%2Br%5E2%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The distance he walks from point r to the campsite (Q):<BR>\n" );
document.write( "(10-r)<BR>\n" );
document.write( "the time if he walks at 5 km/h<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810-r%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%2810-r%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Create an equation for the total time paddling and walking<BR>\n" );
document.write( "T(r) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%281%5E2%2Br%5E2%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28sqrt%281%5E2%2Br%5E2%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2810-r%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%2810-r%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "put this on your graphing calc, find the minimum time for some value of r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+5%2C+-1%2C+3%2C+%28sqrt%281%2Bx%5E2%29%2F3%29%2B%28%2810-x%29%2F5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "the distance r is from the point p is on the x axis<BR>\n" );
document.write( "the total time is on the y axis<BR>\n" );
document.write( "Mimimum time is when, point r is .75 km from p and 9.25 km from Q<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );