This problem initially had two parts but now has three.
OK, let’s start with this: let’s assume that we have two, trains, 100 miles apart, each going with 20 mph to the other. A fly travels between them at 50 mph, zig-zagging just before getting smashed between the trains. Question: How far does the fly fly before meeting his ultimate demise?
Got the answer? Good. Now, let’s modify the original problem a little: let’s also assume that the wind blows with 10 mph from east, and the trains are going on a straight railway, oriented east-west. Relative to the ground, what is the total distance traveled by the fly this time?
Now the third part. Let’s assume that the fly starts from a point between the two trains (let’s say “x miles from the west train”). What would be the value of “x” if the total distance is the same no matter what is the initial direction of the fly?
[update: on the second part, let’s assume that the fly starts from the train from the west. Also – each train has 20 mph ground speed. Finally, another update: I added a third part.]