# Morning commute

ark13
Posers and Puzzles 28 Jun '07 23:23
1. ark13
Enola Straight
28 Jun '07 23:23
You drive to work along a two lane road (one lane each direction) with no passing, stop lights or stop signs. One morning, you encounter no other cars traveling in the same direction as you, either in front of you or behind you. How does your average speed most likely compare with the average speed of the average speeds of the all the other cars on that same road at the same time traveling the same direction (the ones that you didn't encounter)?
2. HandyAndy
Non sum qualis eram
28 Jun '07 23:41
Originally posted by ark13
You drive to work along a two lane road (one lane each direction) with no passing, stop lights or stop signs. One morning, you encounter no other cars traveling in the same direction as you, either in front of you or behind you. How does your average speed most likely compare with the average speed of the average speeds of the all the other cars on that same road at the same time traveling the same direction (the ones that you didn't encounter)?
Average speed of all cars is most likely the same. Cars ahead are either moving at the same speed or accelerating; cars behind are either moving at the same speed or falling behind. In the latter case, speeds should average out.
3. ark13
Enola Straight
28 Jun '07 23:56
Originally posted by HandyAndy
Average speed of all cars is most likely the same. Cars ahead are either moving at the same speed or accelerating; cars behind are either moving at the same speed or falling behind. In the latter case, speeds should average out.
That's the intuitive answer, but I don't believe that's correct. Think about the no-passing restriction.
4. coquette
29 Jun '07 00:27
Well, by no-passing and no-encounters, then i suppose you mean that you are going faster on average than the next car behind you that happens to be slowing all the others down, while you simply may not be catching up to the next car in front because you happen to be going the same speed. however, i don't see where there is enough information in this puzzle to come up with a real solution. i'll be interested to learn what it is if it exists.
5. HandyAndy
Non sum qualis eram
29 Jun '07 01:46
Originally posted by ark13
That's the intuitive answer, but I don't believe that's correct. Think about the no-passing restriction.
But if other cars are either maintaining or increasing their distance from me, either ahead or behind, why would the no-passing restriction come into play?
6. 29 Jun '07 09:182 edits
I think what the question might be getting at is that cars don't all necessarily travel at the same speed. Therefore a no-passing restriction reduces the average speed, as the faster cars are slowed down.

If you encounter no vehicles, then you are unaffected by the restriction. So your speed is probably higher than average (assuming you have an average speed car to start with).

But it could just be that the question isn't very clear ðŸ™‚
7. wolfgang59
29 Jun '07 22:03
Given the limited information the answer must be that traffic behind is travelling at your average speed (or less) an that traffic in front is travelling at your average speed (or more).

To be pedantic one cannot say ANYTHING about average speed of other traffic unless we have an initial start position and know how long scenario will exist for (forever?)

I failed Fluid Dynamics but I think the solution to the (correctly set) problem is in that branch of Math.
8. ark13
Enola Straight
29 Jun '07 23:52
I made this up myself, and I just realized I phrased it badly. What I meant to say was "how does your average speed compare to the speed that the cars would go if they were alone on the road. The answer I was looking for is that you're most likely to be going slower than the average cars. Since multiple cars are likely to be limited to a lower speed by a single car they are following then you're probably going lower than the intended speed of the other cars.

9. HandyAndy
Non sum qualis eram
30 Jun '07 01:35
Originally posted by ark13
I made this up myself, and I just realized I phrased it badly. What I meant to say was "how does your average speed compare to the speed that the cars would go if they were alone on the road. The answer I was looking for is that you're most likely to be going slower than the average cars. Since multiple cars are likely to be limited to a lower speed by a si ...[text shortened]... ntended speed of the other cars.

Well, at least it's a good way to avoid getting speeding tickets.
10. coquette
30 Jun '07 01:37
Originally posted by ark13
I made this up myself, and I just realized I phrased it badly. What I meant to say was "how does your average speed compare to the speed that the cars would go if they were alone on the road. The answer I was looking for is that you're most likely to be going slower than the average cars. Since multiple cars are likely to be limited to a lower speed by a si ...[text shortened]... ntended speed of the other cars.

no apology needed. i think multiple answers went directly to that point, including mine.

So, here's one along the same lines: If a cat chases a dog around a bush, what kind of a cat is it likely to be? in fact, it helps to think about what kind of a dog is being chased and why.
11. HandyAndy
Non sum qualis eram
30 Jun '07 02:11
Originally posted by coquette
no apology needed. i think multiple answers went directly to that point, including mine.

So, here's one along the same lines: If a cat chases a dog around a bush, what kind of a cat is it likely to be? in fact, it helps to think about what kind of a dog is being chased and why.
The cat is a 500-pound Bengal tiger and the dog is a six-pound Chihuahua. Obviously, the cat has a fondness for Mexican food.
12. 06 Jul '07 02:55
...if you put the cheese on the bread first and then the ham is it not a cheese and ham sandwhich ?...so why is it always called a ham and cheese sandwhich ?...and does it make a difference if you walk around a bush while