"Imagine she travels 1 km in 1 minute for the first 2 minutes, then 1 km in 2 minutes, then 1km in 5 minutes. She travels at a speed of 1km/mx2, +0.5 km/m, +0.2km/m. Add these and divide by 4 her average speed is 0.675 km per minute or 40km/h
Then the return journey, say it takes her 3 minutes to travel 1km, then 1 minute to travel 0.5km, a minute to travel 0.1 km and in the last minute she travels 1.4km. Add these up you got 0.33, 0.5, 0.1 and 0.4, average speed 0.583 km/m or 35km/h"
Here is the flaw. You need to average the speeds for each minute of travel.
Out bound = 1+1+.5+.5 (cause it's for 2 minutes) +.2+.2+.2+.2+.2 (it's for 5 minutes). When averaging values, you must have a common factor for the average, not just the scale, but the actual factor. In this case it is a minute. So you add all those up and divide by 9 (total minutes) and you get the average speed.