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Edited to expose all but the very kernel of the answer. Please see http://meta.puzzling.stackexchange.com/a/1424/
Rob Watts
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The bird's speed is 5 mph. If

the speed of the wind across the ocean is greater than or equal to 1 mph towards the direction the bird is flying*, the overall speed of the bird will be greater than 6 mph,

and it can easily reach the other side of the ocean without resting.

So that means

the speed of the ocean wind at that time must have been at least 1 mph in the same direction the bird was flying.

And hence the bird reached the other side of the ocean without resting.

This picture illustrates the point:

*Or greater than or equal to √2 mph to any angle not more than 45˚ from the direction of bird's flight. If greater than 45˚, it needs to be more than √2 mph, depending on the angle.

AeJey
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