Question 50340
George fell asleep halfway through the journey. 

George was awake the 1st half of the journey.
At this point he fell asleep.

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When he awoke, he still had to travel half the distance that he had traveled while sleeping.

He had been sleeping half of one-half of the journey.
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 For what part of the entire journey had he been asleep?

He was asleep half of one-half of the journey, or 1/4 of the 
total journey.

Cheers,
Stan H.