Originally Posted by
wphamilton
The two situations are different, that's the point. Each calculation is correct and equivalently calculated: total distance over time. By "average over time" he means consider riding a certain time at each speed. By "average over distance" he means consider riding a certain distance at each speed. The variable values are different, so the answers are different, but the calculation is the same. There is no "weighted average" involved. 15 is what I told you, and you confirmed it, with the normal delta s/delta t arithmetic.
His point was speculating that people sometimes think of "over time" when the real situation is "over distance" and that's where they make the mistake.
15 is what you told me and I confirmed, however when you restated the example, you changed it from riding 20mph for 30 min to riding 20mph for one hour which changed the average speed from 13.34 to 15.
My point is that riding 10mph for 10 miles, followed by 20mph for 10 miles IS NOT an average speed of 15mph. In this example, the average speed is always 20 miles / 1.5 hours = 13.34 mph. You can arrive at that number multiple ways but the average speed is always 13.34 mph.
*** I brought up the weighted average, because the comment that I am addressing stated that somehow simple logic leads us to an average speed of 15mph. I can only assume he arrived at this number because .5 of the ride distance was at 10mph, and .5 was at 20mph... .5 * 10mph + .5 * 20mph = 15. This is not how average speed is calculated and leads you to the wrong number.
What confuses me is this concept of average speed over time and average speed over distance. Both time and distance are factored into average speed already.
Post edit: Ultimately I see what you are saying now that he was using the 15mph as an example of how average speed is often miscalculated. As for your strava calculation, if I am not mistaken, Strava stops the timer when you are not moving so it calculates average speed based on ride time rather than total time.