Driving to Cleveland

Zach and his family were driving into Cleveland for the ball game. Zach fell asleep when they were halfway along the way. When he woke up the distance they still had to go was half as far as they went while he was asleep. For what fraction of the way did Zach catch his Z’s?

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Zach slept for 1/3 of the distance.

x + x/2 = d/2

2x + x = d, so x = d/3.

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