At 12.00 hours, J starts to walk from his house at 6 kmph. At 13.30, P follows…

Concept: When a second person starts later than the first from the same point and moves in the same direction, the gap between them changes at the relative speed - the difference between their speeds. The time needed to reach any target gap equals that target relative distance divided by the relative speed.

1. J starts walking at 12:00 at 6 kmph. By 13:30, when P sets off, 1.5 hours have passed, so J has already covered 1.5 x 6 = 9 km. J is 9 km ahead of the starting point when P begins.

2. P cycles at 8 kmph, faster than J's 6 kmph, so P gains on J at a relative speed of 8 - 6 = 2 kmph.

3. "J is 3 km behind P" means P must be 3 km ahead of J. So P must first close J's existing 9 km lead and then open a further 3 km lead - a total relative distance of 9 + 3 = 12 km.

4. Time for P to cover this 12 km relative distance at 2 kmph = 12 / 2 = 6 hours.

5. Adding 6 hours to P's start time of 13:30 gives 13:30 + 6:00 = 19:30 hours.

Cross-check: At 19:30, J has walked for 7.5 hours (12:00 to 19:30), covering 7.5 x 6 = 45 km. P has cycled for 6 hours (13:30 to 19:30), covering 6 x 8 = 48 km. P is 48 - 45 = 3 km ahead of J, confirming J is 3 km behind P.

So J is 3 km behind P at 19.30 hrs.