Question 50440
Let a = distance travelled while asleep
Let d = total distance travelled
First he travels half the total distance, or d/2
Then he falls asleep
The ratio a / (distance remaining) = 2/1
distance remaining  = a/2
a + (distance remaining) = d/2 (this is known from the problem)
distance remaining = d/2 - a
a/2 = d/2 - a
a + a/2 = d/2
3a/2 = d/2
a = d/3
So, he is asleep for 1/3 of the distance travelled