Annie the Dog would have run 7025 feet by the time she met her owner for the fifth time. This is calculated by summing the distances of each trip she took to and from home, with each subsequent trip being half the remaining distance to her owner.
The question asks us to calculate the total distance that Annie the Dog ran by the time she met her owner for the fifth time. Given that she started running while they were about half a mile from home (2400 feet) and each time she came back, she met her owner at a point halfway from where she had left them, we can deduce the following:
- Annie first runs to the home (2400 feet) and comes back to the halfway point (1200 feet), which is a total of 3600 feet.
- On the next trip, she covers half of the remaining distance (600 feet) and returns, adding another 1200 feet.
- This pattern continues with Annie covering 300 feet, then 150 feet, and finally 75 feet on her subsequent trips, each followed by a return trip to meet her owner at the halfway point.
- The total distance run is the sum of these distances: 3600 feet + 1200 feet + 1200 feet + 600 feet + 300 feet + 150 feet + 75 feet = 7025 feet.
Therefore, the total distance Annie the Dog ran was 7025 feet.