SOLUTION: The chen family went for a hike. they walked one-half of the length of the trail in the mornig. They walked one-third of the remaining distance in the hour after lunch. They walked

Question 65907: The chen family went for a hike. they walked one-half of the length of the trail in the mornig. They walked one-third of the remaining distance in the hour after lunch. They walked half of the distance that remained during the next hour. Then they walked the last 2 miles of the trail. How many miles long is the trail?
Answer by pilly(1) (Show Source): You can put this solution on YOUR website!
The trail is 12 miles long.
The best way to approach this is to start from the end of the trail where you know the distance was 2 miles.
This was half of the remaining distance so that makes a total of 4 miles so far.
Those combined were 2/3 of the remaining distance so that makes 6 miles total so far.
That entire amount was half the trail which is then 12 miles.

Consider a line representing the respective walking segments:
~~~~~~~~~~1/2~~~~~~~~~~~~~~~~1/3~~~1/2~~~2
|-----------------------------------|---------|--------|--------|
~~~~~~~~6miles~~~~~~~~~~~~~2 miles~~~2 miles~~~2 miles
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