A walks around a circular field at the rate of one round per hour, while B…

Concept: when two people move around the same circular track in the SAME direction, starting together from the same point, the faster one first crosses (catches up with) the slower one only after covering exactly one complete lap more than the slower one has covered. If both speeds are given in rounds (laps) per hour, the time needed for this is: time = 1 lap divided by relative speed, where the relative speed (same direction) = faster runner's speed minus slower runner's speed.

Applying this to A and B:

1. A's speed = 1 round per hour; B's speed = 6 rounds per hour, both starting together at 7.30 am in the same direction.

2. Relative speed of B with respect to A = 6 - 1 = 5 rounds per hour.

3. Time for B to gain one full round over A = 1 round divided by 5 rounds per hour = 1/5 hour = 12 minutes.

4. Adding this to the start time: 7.30 am + 12 minutes = 7.42 am.

Cross-check: in 12 minutes (1/5 hour), A covers 1 x 1/5 = 1/5 of a round and B covers 6 x 1/5 = 6/5 of a round. B's distance exceeds A's by 6/5 - 1/5 = 1 full round, confirming B has gained exactly one complete lap on A at this instant -- so this is indeed their first crossing.

Hence, A and B first cross each other at 7.42 am.