Nullarbor Plain puzzle I have the following puzzle I'm trying to solve:
"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'm not quite sure what to do here. Given what the actual train tracks look like I'll assume that they are a straight line from east to west (from left to right). But where is the man? Above or below this line? Also, the train might be out of reach, or am I missing anything? Thanks for helps.
 A: (This is not an answer, but it is too big for a comment, so I am posting it CW.)
Rotate the problem so that the track runs west to east and the man is south of it by distance $s$, and he hears the whistle in a northwesterly direction. Presumably the man is slower than the train; say the man's speed is 1 and the train's is $V$ with $V>1$.
An obvious strategy is to walk due north to point $N$.
The only other direction that is not an obvious loser is northeasterly to some point $d$ units east of $N$. The man has traveled a total of $s'=\sqrt{d^2+s^2}$, which takes longer, but only by $s' - s$. The train has traveled an extra $d$ distance.  $d<s'$, but we might have $d > s'-s$, and if ${d\over s'-s} > V$, then the man gets a benefit from going northeast. So it's at least conceivable that the man could get a win by doing this.
A: I was solving the same problem and then I got impatient as to what the answer could possibly be, given that there is very little detail given in this problem. Then I came across this old question on StackExchange, and then this article as well. As it turns out, the one line answer to this question is that the man walks in a direction directly perpendicular to the the direction from which he hears the train whistle! I did check and it made sense. His relative velocity towards the train should be directed directly towards the train's direction of whistle so that he makes the optimal trip to catch it, and then the rest will simply follow with some elementary trigonometry.
Sometimes, we can't even fathom that the given information is truly sufficient to give an accurate answer, but that's the way it is in the world of problem solving!
