SOLUTION: while taveling to his granmothers for easter, george fell asleep halfyway through the journey. when he awoke, he still had to travel half the distance that he had traveled while sl

Algebra ->  Human-and-algebraic-language -> SOLUTION: while taveling to his granmothers for easter, george fell asleep halfyway through the journey. when he awoke, he still had to travel half the distance that he had traveled while sl      Log On


   

Question 50440: while taveling to his granmothers for easter, george fell asleep halfyway through the journey. when he awoke, he still had to travel half the distance that he had traveled while sleeping. For what part of the entire jorney had he been asleep
can you please explain to me how you found the answer
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
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