But seriously, folks, is this one going to be as useful / used as the
newbies forum? Anyone with any actual POSERS or PUZZLES, perhaps?
Just wondering.

Sort off. We both like the puzzles that were cropping up in the
general forum and thought it would be wise to have a dedicated forum.

Here's a quickie...

I travel from my home, up a straight road to my work at 30mph. How
fast would I need to drive home in order to make my average speed
for the round trip 60mph?

You can't unless you take a different route home. If you went straight home, the round trip
would only be twice the distance of your trip into work, so for the round trip to be completed
at double the average speed of the trip into work, it would have to take the same amount of
time as the trip into work, leaving you no time at all to get home.

That is correct. If the trip to work was 30 miles, it would take an hour
to get to work. Since the round trip would then be 60 miles, you would
have to make the round trip in a hour to average 60 miles per hour
round trip. But you've already spent an hour gettin to work, you big
slacker. The best you can do is approach the limit of a 60 mph
average.

Suppose the distance from home to work is 60 miles. Then it would
take you 60 / 30 mph = 2 hours to travel to you work.
If you then go back home the total distance you travel is 120 miles. If
you do this at an averge of 60 mph it would take 120 / 60 = 2 hours!

So the conclusion is that you have to travel back home in zero
seconds, so your speed should be infinite!?

I've read all the responses, and I think Andrew (latex bishop) was
correct all along. It is 90mph and NOT 120 mph. Here's why:

You are looking for an average of 60mph.
Both distances are the same.
You travel towork at 30mph UNDER the average desired.
Therefor, you must travel home at 30 mph OVER the average desired.

Anyone, is this flawed? I think Andrew's formula proves it to be correct.

Joke? If so, you can explain the flaw in this reasoning better than I am about to.

If not, the flaw is that, taking 'average' to mean 'mean', average speed is the sum of each
speed multiplied by the TIME spent at that speed, divided by total TIME. If instead we
performed the calculation using DISTANCE instead of TIME, the result would be not the mean
speed, but the 'mean square speed' divided by the average speed. An interesting number
perhaps, but not as widely used as mean speed on its own.

If you're talking about median or modal speed, of course, those can never be higher than
30mph unless you take a detour. But that's another matter...