Let’s work backwards, and use hours instead of distance for ease (assume the plane travels at a constant speed for our purposes).

Let’s say when she woke up, she had 1 hour left in her flight. That’s half of the time she was sleeping so she must’ve slept for 2 hours.

She first fell asleep halfway through the flight, so she was awake for the first 3 hours, then slept for 2, then was awake for the last 1.

She was asleep for 2/6 = 1/3 of the trip.

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