MHB Distance Between Erie & Buffalo: 17 to 83 Miles

  • Thread starter Thread starter tkhunny
  • Start date Start date
AI Thread Summary
Erie and Buffalo are not 70 miles apart, as indicated by highway signs showing Erie at 17 miles and Buffalo at 87 miles. Subsequent signs further clarify the distances, with one indicating Erie at 11 miles and Buffalo at 81 miles. The discussion highlights that road signs reflect road distances, not geographical distances, suggesting a potential T-junction scenario. Despite the signs being exact, the linear travel assumption complicates the interpretation of distances. Ultimately, the conclusion is that the road distance from Erie to Buffalo could be as much as 92 miles, depending on the route taken.
tkhunny
Messages
256
Reaction score
0
1) Erie and Buffalo are NOT 70 miles apart.

2) Correct sign on the highway reads:

Erie: 17 miles
Buffalo: 87 miles

3) Four miles later, another correct sign reads:

Erie: 13 miles
Buffalo: 83 miles

4) If I am going to Erie, what will the sign say about Buffalo when I get there?

Enough information? Too easy?
 
Mathematics news on Phys.org
I think steps 2 and 3 imply that you, Erie, and Buffalo are colinear, but this is not an option due to 1. My reasoning is that if when you move 4 miles, you are exactly 4 miles closer to Erie, it implies you are going straight towards Erie (shortest path in a plane) and so there is no way you can also be 4 miles closer to Buffalo unless you are also going straight towards Buffalo. When you say "four miles", is it distance traveled or displacement? How accurate are the signs?

My first thought was that this was an ellipse problem, but I am no longer sure.. tricky challenge!​
 
Clarifications:

Signs are exact.
Travel is linear.
Travel Distance = Displacement -- No turns and no rifts in the space/time continuum.

There may not be enough information.

3a) 2 miles later, a correct sign reads:

Erie: 11 miles
Buffalo: 81 miles

3b) After that, there are no more such signs.
 
Last edited:
tkhunny said:
Clarifications:

Signs are exact.
Travel is linear.
Travel Distance = Displacement -- No turns and no rifts in the space/time continuum.

There may not be enough information.

3a) 2 miles later, a correct sign reads:

Erie: 11 miles
Buffalo: 81 miles

3b) After that, there are no more such signs.
Road signs show road distances, not geographical distances. Perhaps at 11 miles from Erie, the road comes to a T junction. If you turn left it is 11 miles to Erie, if you turn right it is 81 miles to Buffalo. From Erie to Buffalo it is then 11+81=92 miles.
 
Opalg said:
Road signs show road distances, not geographical distances. Perhaps at 11 miles from Erie, the road comes to a T junction. If you turn left it is 11 miles to Erie, if you turn right it is 81 miles to Buffalo. From Erie to Buffalo it is then 11+81=92 miles.

TKhunny specified no turns, though, so the road has to be straight, which sort of implies that road distance is the same as geographical distance (on the Earth's surface, anyway).
 
Opalg has it. Road signs give mileage on the road, whether the road turns or not. More of a Y-junction, though. Check out I-86 and I-90 between Erie and Buffalo, 11 miles East of Erie. Coming West on I-86 we see the signs that are maybe a little confusing. There is very little turn to Erie and quite a sharp turn toward Buffalo.

If there were such a sign when entering Erie, it might say, "Buffalo is 92 miles BEHIND YOU!"

Thanks for playing!
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Back
Top