Geometry, calculus, and angle theorems are used in this challenge.
You are going on a vacation to an island in a sea. It’s a long journey. First, you have to drive to the sea. You park your car, take off your motorboat which you carried on top of it, and embark onto the sea. Then, you take your boat up to the island, park it, and walk up to your cottage. The sea and island are both ellipses, Whose foci are co-linear and point to your starting point. The sea and island both have their major axes twice the length of their minor axes, and you are a minor sea axis away from the closest point to the sea. Driving is 3 times faster than boating, which is thrice as fast as walking. The sea has only one island, and is 8 ninths water. What is the quickest route to your cottage?