John goes for a run. from his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. he continues north at a speed of 12.0 km/h for the next 30.0 min. he then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. then he jogs south for another 20.0 min at 8.0 km/h. he walks the rest of the way home.

jogs north for exactly 5.0 min at an average speed of 8.0 km/h.

Convert velocity from km/h to km/min

V = 8.0 km/h * 1h/60min = 2/15 km/min
Distance = V*t = [2/15 km/min]*5min = 2/3 km

He continues north at a speed of 12.0 km/h for the next 30.0 min.

Again convert km/h to km/min

V = 12.0 km/h * 1h/60min = 1/5 km/min
D = V*t = [1/5 km/min]*30min = 6 km

He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min.

Position before turning around
X = 2/3 km + 6 km = 20/3 km North

D = V*t = 15.0 km/h *(1/4 h) = 15/4 km

New position: 20/3 km North - 15/4 km South =  35/12 km North

Then he jogs south for another 20.0 min at 8.0 km/h.

D = V*t = 8.0km/h * [1/3 h] = 8/3 km

New position 35/12 km North - 8/3 km South = 3/12 = 1/4 km North

Total distance jooged = 20/3 km + 15/4 + 8/3 km  = 157/12 km =  13.08 km ≈ 13.1 km

He walks the rest of the way home

He will have to walk 1/4 km = 0.25 km to get home after he finishes jogging