I suspect that was meant to be a joke ... but it is
even more fun if we take it seriously.
As we all know, you can find the average speed by
averaging the instantaneous speed with respect to time:
∫ s dt
〈s〉 = --------- [1]
∫ dt
Now the fun part is that you can find the average
inverse speed by averaging the instantaneous inverse
speed with respect to *distance*
∫ 1/s dx
〈1/s〉 = ---------- [2]
∫ dx
Equation [1] is useful if you want to find the total
distance traveled. That's the numerator in equation [1].
Equation [2] is useful if you want to find the total
elapsed time. That's the numerator in equation [2].
Hint: Both numerators are kinda obvious if you think
about the dimensions.
The singularity in equation [2] can be taken as a
warning. If you are trying to finish a race in the
least amount of time, going slowly even for a rather
short distance is devastating. This is actually
true, and quite noticeable if you do the experiment.
To say the same thing in slightly more positive terms,
if there is a fast half of the course and a slow half
of the course (perhaps due to hills) you can gain a
lot more by speeding up the slow half by 1 mph than
you can by speeding up the fast half by 1 mph. Also
true and quite noticeable.
====================
This occasionally comes in handy as an answer to the
athlete who thinks physics equations could not possibly
explain anything he is interested it.