SOLUTION: "Halfway through her bus trip from Savannah to Jacksonville, Gertrude fell asleep. When she awoke, she still had to travel half o the distance she traveled when asleep. For what

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Question 171241: "Halfway through her bus trip from Savannah to Jacksonville, Gertrude fell asleep. When she awoke, she still had to travel half o the distance she traveled when asleep. For what fraction of the trip was Gertrude asleep?"

I have tried drawing diagrams and setting up equations, and nothing has worked. Please help me with this one. Thanks so much!
Found 2 solutions by Mathtut, scott8148:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the entire distance travel x and the amount she slept for y. therefore 1/2y would be the distance she still had to travel.
:
since she fell asleep half way thru the trip we have this formula:
1/2x-system%281=e%2C1=n%2C1=t%2C1=i%2Cl=r%2Cl=e%29
y------system%28l=t%2Cl=r%2Cl%2Cl=i%29
1/2y----system%28l%2Cl=p%29
:
y+1/2y=1/2x...multiply by 2
:
2y+y=x
:
3y=x
:
highlight%28y=%281%2F3%29x%29.......so she fell asleep for1/3 or 33% or 33/100 of the trip

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=fraction asleep

"Halfway through her bus trip from Savannah to Jacksonville, Gertrude fell asleep"
__ so she fell asleep at the start of the 2nd HALF of the trip

"When she awoke, she still had to travel half o the distance she traveled when asleep"
__ so x+(1/2)x=1/2

multiplying by 2 __ 2x+x=1 __ 3x=1

dividing by 3 __ x=1/3