document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907484>Question 907484</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve this word problem: Joe is kayaking on a lake.  He is 2 miles from the nearest point on the shoreline.  From there he is 5 miles from his car.  He can average 2 MPH kayaking and 3 MPH walking on the shore.   He wishes to get to his car quicker so he heads to the shore at an angle towards his car. \r<BR>\n" );
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document.write( "There is a model using a right triangle with 2mi on the 90degree side. x is the length of the bottom and I don't know the hypotenuse length either. I need to find both x and the hypotenuse.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550517 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joe's kayak is on the lake at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K ALIGN=MIDDLE  ALT=\"K\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for KAYAK).<BR>\n" );
document.write( "The nearest point on the shore is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for NEAREST),<BR>\n" );
document.write( "and Joe's car is next to the shoreline at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for CAR).<BR>\n" );
document.write( "Joe will land the kayak at shoreline point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for LANDING),<BR>\n" );
document.write( "which is somewhere between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=miles ALIGN=MIDDLE  ALT=\"miles\"   DISABLED_style= \"max-width:90%; height:auto;\" > from point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > (for hypotenuse) from point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K ALIGN=MIDDLE  ALT=\"K\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-x ALIGN=MIDDLE  ALT=\"5-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from point  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-1%2C7%2C-1%2C3%2C%0D%0Aline%28-1%2C0%2C7%2C0%29%2Ccircle%285%2C0%2C0.05%29%2C%0D%0Atriangle%280%2C0%2C0%2C2%2C1.79%2C0%29%2C%0D%0Arectangle%280%2C0%2C0.2%2C0.2%29%2C%0D%0Alocate%285.5%2C0%2Cshoreline%29%2C%0D%0Alocate%28-0.1%2C0%2CN%29%2Clocate%28-0.1%2C2.3%2CK%29%2C%0D%0Alocate%281.7%2C0%2CL%29%2Clocate%284.9%2C-0.1%2CC%29%2C%0D%0Alocate%280.1%2C1.1%2C2%29%2Clocate%280.8%2C0.3%2Cx%29%2C%0D%0Alocate%280.8%2C1%2Ch%29%2Clocate%283%2C0.3%2C5-x%29%2C%0D%0Aarrow%282.8%2C0.15%2C1.8%2C0.15%29%2Carrow%283.8%2C0.15%2C5%2C0.15%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The Pythagorean theorem tells us that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%28x%5E2%2B2%5E2%29=sqrt%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"h=sqrt%28x%5E2%2B2%5E2%29=sqrt%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The time (in hours) for Joe to cover that distance kayaking at 2 MPH is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2B4%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The time (in hours) for Joe to cover the distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-x ALIGN=MIDDLE  ALT=\"5-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > walkking at 3 MPH is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-x%29%2F3 ALIGN=MIDDLE  ALT=\"%285-x%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total time (in hours for Joe to go from point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K ALIGN=MIDDLE  ALT=\"K\"   DISABLED_style= \"max-width:90%; height:auto;\" > to point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28x%29=sqrt%28x%5E2%2B4%29%2F2%2B%285-x%29%2F3 ALIGN=MIDDLE  ALT=\"t%28x%29=sqrt%28x%5E2%2B4%29%2F2%2B%285-x%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
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document.write( "That much you would reason, regardless of your math class level and instructor preferences.<BR>\n" );
document.write( "From this point on, what your instructor wants depends.<BR>\n" );
document.write( "If you are being pushed to use and abuse a graphing calculator, you may be expected to graph the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28x%29 ALIGN=MIDDLE  ALT=\"t%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find its minimum.<BR>\n" );
document.write( "If you are studying calculus, you may be expected to calculate the derivative of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28x%29 ALIGN=MIDDLE  ALT=\"t%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the point where the derivative is zero and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28x%29 ALIGN=MIDDLE  ALT=\"t%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is minimum:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dt%2Fdx=%281%2F2%29%281%2F2sqrt%28x%5E2%2B4%29%29%282x%29%2B%281%2F3%29%28-1%29=x%2F2sqrt%28x%5E2%2B4%29-1%2F3=%283x-2sqrt%28x%5E2%2B4%29%29%2F6sqrt%28x%5E2%2B4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dt%2Fdx=0 ALIGN=MIDDLE  ALT=\"dt%2Fdx=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-2sqrt%28x%5E2%2B4%29=0 ALIGN=MIDDLE  ALT=\"3x-2sqrt%28x%5E2%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2sqrt%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"3x=2sqrt%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=4%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"9x=4%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=4x%5E2%2B16 ALIGN=MIDDLE  ALT=\"9x=4x%5E2%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2=16 ALIGN=MIDDLE  ALT=\"5x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16%2F5 ALIGN=MIDDLE  ALT=\"x%5E2=16%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2816%2F5%29%7D%7D+---%3E+%7B%7B%7Bx=4%2Fsqrt%285%29=4sqrt%285%29%2F5 ALIGN=MIDDLE  ALT=\"x=sqrt%2816%2F5%29%7D%7D+---%3E+%7B%7B%7Bx=4%2Fsqrt%285%29=4sqrt%285%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=about+1.79%29 ALIGN=MIDDLE  ALT=\"highlight%28x=about+1.79%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(Joe should aim for landing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281.79%29 ALIGN=MIDDLE  ALT=\"highlight%281.79%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles from point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now that we have found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for Joe,<BR>\n" );
document.write( "he has all the side lengths for right triangles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NKL ALIGN=MIDDLE  ALT=\"NKL\"   DISABLED_style= \"max-width:90%; height:auto;\" > (pictured) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NKC ALIGN=MIDDLE  ALT=\"NKC\"   DISABLED_style= \"max-width:90%; height:auto;\" > (imagine it),<BR>\n" );
document.write( "so I would let Joe figure out the angles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NKL ALIGN=MIDDLE  ALT=\"NKL\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NKC ALIGN=MIDDLE  ALT=\"NKC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LKC ALIGN=MIDDLE  ALT=\"LKC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that he can use to get going in the right direction. </SPAN>\n" );
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