The persons start walking at a steady pace of 3 km/hour from a road 1 intersection along two roads that make an angle of 60° with each other. What will be the (shortest) distance separating them at the end of 20 minutes ?

Each person walks at 3 km/h for 20 minutes (1/3 hour), so each covers distance = 3 × (1/3) = 1 km. The two walkers and the intersection form a triangle with two equal sides of length 1 km and an included angle of 60°. Applying the Law of Cosines, the straight-line separation c satisfies c^2 = a^2 + b^2 − 2ab cos(60°) = 1^2 + 1^2 − 2·1·1·(1/2) = 2 − 1 = 1, hence c = 1 km. This straight-line value is the shortest distance between them, so the correct choice is option 4) 1 km.