
Optimization problem #4
A small island is 2 km off shore in a large lake. A woman on the island can row her boat at 10 km/h and can run at a speed of 20 km/h. If she rows to the closest point on the straight shore, she will land 6 km from a village on the shore. Where should she land to reach the village most quickly by a combination of rowing and running?

You need to draw a picture for this to understand it completely.
You need to minimise a function of time as a combination of running and rowing.
I.e f(x) = Runing Time + Rowing Time.
I get $\displaystyle f(x) = \frac{6x}{20}+\frac{\sqrt{x^2+2^2}}{10}$
Then solve for $\displaystyle f'(x) = 0$