B Explore Nullarbor Plains: Walking North to Find the Track

[StatOnTheSide]

TL;DR Summary

There's a puzzle from the book "Thinking Mathematically" by Mason and Burton.

"A man lost on the Nullarbor Plain in Australia hears a train whistle due west of him. He cannot see the train but he knows that it runs on a very long, very straight track. His only chance to avoid perishing from thirst is to reach the track before the train has passed. Assuming that he and the train both travel at constant speeds, in which direction should he walk?"

I guessed that if he knows the track, then he should just walk perpendicular to it. However, it is not clear if he knows where the track is. In fact, not much is given in the problem except that he hears the train's whistle from the west.

Based on this article, the answer seems to be that he walks directly perpendicular from the direction of the train's whistle which means he just walks north! Why is that?

 

[mfb]

At least based on the sketch it's just "somewhere in the west", not directly west. And you know (or hear) on which side of the track you are, hopefully, so you don't walk away from it.

Going straight towards the track can make you miss the train if you can still reach it under an angle. The article finds the ideal angle for that: The angle where you reach the train with the minimal possible speed.