Trying to gauge how smart Massassi is by asking pointless theoretical questions with no practical purpose that most people could never be bothered to think about (Believe it or not, few people think staring at numbers all day is fun), so here is a much simpler question with an actual real world use.

You are driving down a 2 mile long stretch of road. You travel the first mile at 30 miles per hour. How fast must you drive for the second mile to average 60 miles per hour?

Mmmm harmonic means...

You`ll be unable to. You`ll need to travel through whole 2 miles for 2 minutes to have 60 mph average speed, but you already spent all of those 2 minutes on driving through first mile at 30 mph.

That's easy. To average 60 mph on the last mile, you'd have to travel at 60 mph.

Right?

[edit] I don't know.

hmmm, for your average speed to be 60, you would need to cover the 2 miles in 2 minutes. Because the first mile at 30 mph already takes 2 minutes by itself, there is no speed fast enough to make your average speed 60 over the 2 miles. (i think :-\ )

/edit
(or pretty much exactly what shade said)

30mph for the first mile and 90mph for the second mile. 30+90/2=60mph average

<edit>
after reading it again, you'd have to travel 60mph to average 60mph on the second mile.

haha
</edit>

It takes you 2 (60/30) minutes to travel the first mile.

Average speed = (Total distance)/(Total time) or S = D/T.

60mph=2miles/x.

x = 0.03h = 2 minutes.

Wait, what?

It's 60mph.

Multiple answers for multiple interpretations!

1. Assuming instant change in velocity when reaching the second mile, you'd have to go 90mph to average 60mph for the entire 2 miles.
2. Assuming instant change in velocity when reaching the second mile, you'd have to go 60mph to average 60mph for the second mile.
3. Assuming you'd have to accelerate over a period of time, we'd need to know the acceleration of the car to calculate how fast you'd have to be going by the end of the road to average 60mph for the entire 2 miles.
4. Assuming you'd have to accelerate over a period of time, we'd need to know the acceleration of the car to calculate how fast you'd have to be going by the end of the road to average 60mph for the second mile.

I think that mostly covers the possibilities :p

(Edit: except when I'm totally wrong. weeee)

I love you.

No, the answer is infinity. To average sixty miles per hour, you must cover 2 miles in 2 minutes. You already used 2 minutes going to the first mile! Doh!

Sounds like you need a car that can go faster than 30mph in its first mile. What kind of crappy car do you drive anyway?

Isuwen is right. You don't average the speeds from each hour to find the average speed, you divide the total distance by the total time.

And I fail! Rock on.

As for my excuse: I haven't done proper math in 2 years.

Aw. But the question was pretty simple, to be honest.

It`s another one of trick problems, which are solved more by common sense, then anything else.

But...

Sorry. It`s really a trick question.

If it`s of any consolation, this is another example of sophism.

Yet you don't understand 0.999... = 1.

(As in, I don't think you knew the answer either)

Matty, I posted answer first - I had noone to copy it from.

And I`m not going to argue about 0.9(9) anymore. Read my post in the appropriate thread, please.

As I said, I don't think you knew the answer (GOOGLE LOL).

And that's fine, you don't need to argue it. Not like there's anything to argue anyway (because you were wrong).

Algebra gives me no solution and algebra is always right!

So it's impossible!