[perching_aix]

Of course.

My math only "checks out" if you accept and account for the additional assumption I made there: that the datapoints provided in the question have been rounded or were low resolution from the get-go.

The motivation behind this assumption is twofold: the numbers in the question are awfully whole (atypical for any practical problem), and that just the rote derivation of it all doesn't produce very interesting results (gives you the infinite speed answer). :)

Try introducing some error terms and see how the result changes! It's pretty fun, and it's how I was able to eek out that 41 mph result in the end.

[swores]

Considering the first mile would need to have been faster than 23mph for your 41mph to give an average of 30... your answer is either completely wrong, or is "if we pretend that the numbers are completely different to what they are then my answer is right", either way it just seems pointlessly wrong rather than pretty fun. But I guess good for you if you enjoyed working out that answer.

[perching_aix]

I can appreciate if someone doesn't (or if most people don't, even) see the fun in this, sure.

> Considering the first mile would need to have been faster than 23mph

That said, note that it's not just the up-leg's average speed that's been provided (15 mph), but also the distance as you say (1 mile). If you explore the error term for both of these, you'll see that it's not necessary to go at the ludicrously high speed of 23 mph after all. """15 mph""" (15.444... mph) will do just fine.

[swores]

If you go as far as assuming the mile distance is wrong then the entire question is pointless, maybe they've already travelled more than two miles and they need to go backwards to average 30mph! At that point literally any number is just as correct as 41 is...

[perching_aix]

It does allow for making any number between 40.833546516585657030783661635542 (exact) and ∞ work, 41 just being the lowest whole number that works. Travelling backwards, being arbitrarily wrong, or any arbitrary number working doesn't fit these new constraints still, however.