- 29 Sep '02 01:10Sort 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?

-Chris - 29 Sep '02 09:54You 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. - 29 Sep '02 10:00That 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. - 30 Sep '02 12:36Suppose 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!? - 03 Oct '02 18:13I'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.

Coyote - 03 Oct '02 20:47"Both distances are the same."

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...