Annie is running a trail that is 4
1
2
miles long. She ran the first
2
3
of the distance. Then the trail became very steep, so she slowed down to walk. Annie walked for
1
2
of the remaining distance and then ran again for the rest of the way. How far did Annie walk?
Annie ran the first 4/3 miles of the trail.
The remaining distance is 4 - (4/3) = 8/3 miles.
Annie walked 1/2 of the remaining distance, which is (1/2) * (8/3) = 4/3 miles.
Therefore, Annie walked a total of (4/3) + (4/3) = 8/3 miles. Answer: \boxed{2 \frac{2}{3}} miles.
To find the distance that Annie walked, we need to calculate the remaining distance after she ran the first 23 of the trail.
Total distance of the trail = 4 1 2 miles.
Distance ran by Annie = 2 3 of the trail = (2/3) * 4 1 2 = 8 2 3 miles.
Remaining distance = Total distance - Distance ran
Remaining distance = 4 1 2 - 8 2 3
To subtract mixed numbers without borrowing, we need to convert them to improper fractions.
4 1 2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
8 2 3 = 8 + 2/3 = 24/3 + 2/3 = 26/3
Remaining distance = 9/2 - 26/3
To subtract fractions, we need to have the same denominator.
Converting the denominators to a common denominator of 6:
9/2 = (9/2) * (3/3) = 27/6
26/3 = (26/3) * (2/2) = 52/6
Now we can subtract:
Remaining distance = 27/6 - 52/6
Remaining distance = (27 - 52)/6
Remaining distance = -25/6
Since the result is negative, Annie did not have to walk any more distance after running.
Therefore, Annie walked 0 miles.