Final answer:
Mark breaks a 9-hour drive into three segments with the given hours, which when added together, approximate to 4.17 hours. The remaining third segment's duration is found by subtracting this number from the total drive time, resulting in the third segment being 4.83 hours long.
Step-by-step explanation:
Mark breaks up a 9-hour drive into three segments: 2 1/2 hours, 1 hour, and 2/3 of an hour.
First, add the time for each segment:
2 1/2 hours + 1 hour + 2/3 hour = 2.5 hours + 1 hour + 0.67 hours = 4.17 hours.
However, since the drive is 9 hours in total and we've only accounted for 4.17 hours, we need to find the length of the third segment Mark has not yet traveled.
To do this, subtract the time of the completed segments from the total drive time:
9 hours - 4.17 hours = 4.83 hours.
Thus, the length of the third segment that Mark will drive is 4.83 hours.