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Posers and Puzzles

Posers and Puzzles

  1. 28 Sep '02 23:11
    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.

    --Rein
  2. 28 Sep '02 23:21
    This is a subtle hint that all the silly logic problems we're doing
    shouldn't be put in the General forum! Ok.

    So, any more "off-topic" puzzles, guys?

    --Rein
  3. Subscriber Chris
    Site Admin
    29 Sep '02 01:10
    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?

    -Chris
  4. 29 Sep '02 02:38
    I suppose 90mph would be too easy an answer...

    J1: a to b = 30
    J2: b to a = 90

    (30+90)/2 = 60
  5. Subscriber Chris
    Site Admin
    29 Sep '02 02:42
    Yep far too easy. Travelling back at 90mph would give you an
    average speed of 45mph... which is a big hint as to the solution...

  6. Donation Acolyte
    Now With Added BA
    29 Sep '02 09:54
    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.
  7. Donation bbarr
    Chief Justice
    29 Sep '02 10:00
    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.
  8. Donation Acolyte
    Now With Added BA
    29 Sep '02 09:55
  9. Donation Jacko
    Knock, Knock...?
    29 Sep '02 12:34
    120mph you said that 9omph was ave. of 45mph so ave. speed of
    60 would be 120mph.

    David
  10. Donation Jacko
    Knock, Knock...?
    29 Sep '02 12:37
    yes thats it 30mph is a mile every 2 mins. and 120 mph would be a
    mile in 30 seconds giving you an average speed of 1 mile a minute
    (60mph)

    wow i got it!!!

    David
  11. Donation Acolyte
    Now With Added BA
    29 Sep '02 16:29
  12. 30 Sep '02 12:36
    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!?
  13. Donation Acolyte
    Now With Added BA
    30 Sep '02 14:17
  14. 03 Oct '02 18:13
    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.

    Coyote
  15. Donation Acolyte
    Now With Added BA
    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...