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. how far will john have to walk until he gets home?

0.25 km

Explanation

Procedure:

Calculate the distance run on each stage as speed × time. First, you have to convert the time to the hours because the speed is in km/h.

Calculations:

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

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

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

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

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) He walks the rest of the way home. how far will john have to walk until he gets home?

Find how far he is from home by subtracting the south distances run from the north distances run. This is:

( 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.

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