SOLUTION: George is going to his grandmother's house. Halfway there, he falls asleep. When he awakens, he learns that he still must travel for half the distance he traveled while asleep in

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Question 421282: George is going to his grandmother's house. Halfway there, he falls asleep. When he awakens, he learns that he still must travel for half the distance he traveled while asleep in order to arrive at his grandmother's house.

We'll assume that George was not driving.

For what fraction of the total trip was George asleep?
Answer by josmiceli(9661) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = distance traveled while he was asleep
After waking d%2F2 is the distance left to travel
+d+%2B+d%2F2 = 1/2 of the whole trip, so
+2%2A%28d+%2B+d%2F2%29+ is the distance for the whole trip
The fraction of this trip that George was asleep was:
+d+%2F+%282%2A%28d+%2B+d%2F2%29%29+
+d+%2F+%282d+%2B+d%29+
+d+%2F+%28d%2A%282+%2B+1%29%29+
Divide top and botom by d
1%2F%282%2B1%29+=+1%2F3
He was asleep for 1/3 of the whole trip