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.

0.25 km

Explanation

Strategy: You have to calculate how far north he got by jogging first at 8km/h during 5 mimutes and second at 12 km / h during 30 min.

Then you have to subtract how many kilometers he came back south at 15 km/h during 15 min and at 8 km/h during 20 min.

Of course you will have to pass the times in minutes to hours by using 1 h = 60 minutes.

These are the calculations:

1) 5.0 min at an average speed of 8.0 km/h (NORTH)

a) time = 5.0 min × 1 hour / 60 min = (1/12) hour

b) distance run = 8.0 km/ h × (1/12) h = (2/3) km North

2)  30 min at 12.0 km/h for the next (NORTH)

a) time = 30 min × 1 hour / 60 min = 0.5 h

b) distance run = 12.0 km/ h × 0.5 h = 6.0  km North

3) 15 min at 15.0 km/h (SOUTH)

a) time =  15.0 min × 1 h / 60 min = 0.25 h

b) distance run = 15.0 km/h × 0.25 h = 3.75 km south

4) 20 min at 8.0 km/h (SOUTH)

a) time = 20 min × 1 h / 60 min = (1/3) h

b) distance run = 8.0 km/h × (1/3) h = (8/3) km

5) Find how far he is from home by subtracting the south distances run from the north distances run:

( 2/3 km + 6.0 km) - (3.75 km + 8/3 km) = 2.25 km - 6/3 km = 2.25 km - 2 km = 0.25 km.

Threfore, he is 0.25 km north from home and that is the distance he will have to walk.