Ms. Jaya takes a train to her granny's place. While on her journey she falls asleep when the train still has twice as far to go as it has already gone.
Halfway through the trip she wakes up when the train stops at a signal. When she finally falls asleep again, the train has yet half the distance to go that it has already traveled. Fortunately, Ms. Jaya wakes up at the end of her trip.
What fraction of the total trip did Ms. Jaya travel sleeping?