Question

Two tourists went on a hike at dawn. One went from a to b and another one went from b to a. They met at noon but did not stop and continued walking maintaining same speed for the whole trip. One finished his hike at 4pm in B and another one came to A at 9 pm. At what hour was dawn that day?

Answer 1

Dawn was at 6 am. Variables a = distance from a to passing point b = distance from b to passing point c = speed of hiker 1 d = speed of hiker 2 x = number of hours prior to noon when dawn is The first hiker travels for x hours to cover distance a, and the 2nd hiker then takes 9 hours to cover that same distance. This can be expressed as a = cx = 9d cx = 9d x = 9d/c The second hiker travels for x hours to cover distance b, and the 1st hiker then takes 4 hours to cover than same distance. Expressed as b = dx = 4c dx = 4c x = 4c/d We now have two expressions for x, set them equal to each other. 9d/c = 4c/d Multiply both sides by d 9d^2/c = 4c Divide both sides by c 9d^2/c^2 = 4 Interesting... Both sides are exact squares. Take the square root of both sides 3d/c = 2 d/c = 2/3 We now know the ratio of the speeds of the two hikers. Let's see what X is now. x = 9d/c = 9*2/3 = 18/3 = 6 x = 4c/d = 4*3/2 = 12/2 = 6 Both expressions for x, claim x to be 6 hours. And 6 hours prior to noon is 6am. We don't know the actual speeds of the two hikers, nor how far they actually walked. But we do know their relative speeds. And that's enough to figure out when dawn was.