How to Read the Signs
Each sign represents an intersection with three directions.
Dutch Flat Trail .7 ^
Canada Trail .3 <-
Heron Trail .3 ->
This means that
if one walks to the right they will be walking on Heron Trail. In 0.3 units, another intersection will be reached. Walk to the left will be on Canada trail and in 0.3 units an intersection will be reached. Walk straight and in 0.7 units an intersection will be reached.
The Confusion
One sign (A) has the following instructions:
Dutch Flat Trail .1 ->
Dutch Flat Trail .7 ->
Walking right, in 0.1 units an intersection will be reached. The second sign in the same direction indicates that the shortest path to the entrance is 0.7 units.
The missing piece of information is whether the sign points to the entrance or an intersection.
This extra information is applied to:
Signs A, B, and C.
The reason that extra distances it isn't listed for E and F is that their shortest paths are direct edges to the entrance and therefore an extra sign is not needed.
Sum it Up
The entrance is
D because it is the only one at the head of three paths.
The letters in the squares are the sign posts. The letters in the circles are the trail names.
The longest non-overlapping path from the entrance is:
D -> B (0.7)
B -> E (0.3)
E -> A (0.7)
A -> F (0.6)
F -> C (0.3)
Total = 2.6 units
Which confirms Gareth McCaughan's AnswerGareth McCaughan's Answer
Bonus
Thanks to @2012rcampion@2012rcampion, I found your sign.
https://goo.gl/maps/AEEYZT9dDx12
