Ira S. answered • 09/27/14

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I will try to explain this without a diagram. Let me first try to describe the diagram. This sounds like it's part of a max/min problem.

Let's call the island point I, draw a vertical line to point P on the shore represented by a horizontal line. 12 mils to the right( could be to the left and it wouldn't matter) is the town point W. I want to find where to land my boat on the shore that would minimize my time, so let's call Point L where I'm going to land. That point L is between P and W,x miles from point P and 12 - x miles from town W.

We need to convert everything into time measurements so R*T=D or T=D/R.

So IP = 6/2 =3

so PL = x/4

so LW = (12 - x)/4

and IL = sqrt(9 + (x^2)/16 ) Pythagorean theorem on triangle ILP.

So I will travel from I to L and then continue on to W. So my function is

T(x) = sqrt(9 + (x^2)/16) + (12 - x)/4

Hope this helped.