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A commuter falls asleep on a train halfway to her destination. She slept until she had half as far to go as she went while she slept. How much of the whole trip was she sleeping?
posted by steven | 11:00 PM
A quarter of the trip
One third of the trip.She is awake for the first half of the trip. Then falls asleep until she has half as far to go as when she slept (i.e. she was awake for the last 1/2 * 1/3 = 1/6 of the trip).1 - 1/2 - 1/6 = 1/3.
Awake for the first half. Asleep for two thirds of the second half, and awake for half of that period which is one third of the second half. Asleep for one third of the journey over all.
A quarter of the trip?
She slept for half the journey.When this person falls asleep, she has half the distance to go.Let's read the line once again 'She slept until she has half as far to go as when she slept'If the above line isn't split - and read as it is - it will sound as 'she slept for next half of her journey from the point she fell asleep' - which is true. Just read, read, read and read again - and try to visualise the line...i'm sure you will arrive at answer 1/2.I don't think 1/4, 1/6 are the correct answers.
@Krish:It reads:'She slept until she had half as far to go as she went while she slept'not'She slept until she has half as far to go as when she slept'and even with your version, I don't make it half the trip
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