# Missing in NY/PA

#### tkhunny

##### Well-known member
MHB Math Helper
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?

#### Bacterius

##### Well-known member
MHB Math Helper
[JUSTIFY]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 travelled 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![/JUSTIFY]

#### tkhunny

##### Well-known member
MHB Math Helper
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:

#### Opalg

##### MHB Oldtimer
Staff member
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.

#### Bacterius

##### Well-known member
MHB Math Helper
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).

#### tkhunny

##### Well-known member
MHB Math Helper
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!