Mr. Hooper goes to work by a private bus that picks up all the company's employees. He gets on at the first stop and has a long way to go, so he usually naps along the way.
Today, Mr. Hooper is particularly tired. He falls asleep when the bus still has twice as far to go as it has already gone.
Halfway through the trip he wakes up as the bus bounces over some bad potholes. When he finally falls asleep again, the bus still has half the distance to go that it has already traveled. Mr. Hooper wakes up at the end of the trip.
What portion of the total trip did Mr. Hooper sleep?
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