Thread: 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

Then solve for