Why should Ed travel at right angles from the original direction of the whistle?

Part 1:

Imagine Ed runs towards a point P on the railway line which is a distance a from him and a distance b from the train. Then he wants to choose this point so that the ratio a/b is as small as possible.

Why is that? If the trains travels at speed v and Ed runs at speed w, then Ed will be saved as long as

av < bw

(This inequality says that Ed takes less time than the train to get to the meeting point.)

Rearranging, what we need is

a/b < w/v

So, no matter v and w, Ed's best chance is to make a/b small.

part 2:

According to the sine rule

a/b = sin A / sin B

now the angle A is fixed, and so we want to make sin B as large as possible. We do this by choosing B = 90º ( sin B = 1). That is, Ed travels at right angles from the original direction of the whistle.