FYKOS Year 36 Series 1 Problem 4 — mountain transport · FYKOS 36 #36.1.4
Physics · mechanics
Problem
There is a town on the slope of a hill whose shape is a cone with apex angle α=90∘. On the other side of the cone, right opposite to the town in the same altitude, lies a train station. Mayor of the town decided to build a road to the station. They can either drill a tunnel or build a road on the surface of the hill. What is the maximum ratio of per-kilometer prices for the tunnel and for the surface road, so that building a tunnel is cheaper? The road can be built anywhere on the hill.