To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the time they meet is 't' hours after A starts at 9.00 am.
Since B starts half an hour later at 9.30 am, B will also travel for 't' hours.
The distance traveled by A in 't' hours is given by DistanceA = SpeedA * t = 6 * t.
The distance traveled by B in 't' hours is given by DistanceB = SpeedB * t = 8 * t.
Since they are traveling in the same direction, the distance between them is given by the difference of their distances traveled:
DistanceAB = DistanceB - DistanceA = 8t - 6t = 2t.
We want to find the time when they meet, which is when the distance between them is zero. So, we set DistanceAB = 0 and solve for 't':
2t = 0
t = 0
Since t = 0, this means they meet at the same time A started, which is 9.00 am.
Therefore, the correct answer is option C) 11.00 am.