Can someone help me with this brainteaser type trivia?

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I've tried to figure this out and I just can't can someone help me, I need to do this for homework.

Desert Training
Somewhere out in the desert the army set up training camps named Arachnid, Feline, Canine, Lupine, Bovine and Porcine.

Arachnid is 15 miles from Canine. Bovine is 12 miles from Lupine. Feline is 6 miles from Porcine. Lupine is 3 miles from Canine. Bovine is 9 miles from Porcine. Bovine is 7 miles from Canine. Porcine is 1 mile from Arachnid. Feline is 11 miles from Lupine. No other pairs are connected by roads.

Find the shortest routes from…
Feline to Bovine
Lupine to Porcine
Canine to Feline
Arachnid to Lupine
Canine to Porcine
Lupine to Bovine
Arachnid to Feline

Please explain how you got that answer, and why you used that method to get your answer.
Thanks!
 
A nice question that is.

The shortest route from one end to the other for each of the pairs:
Feline to Bovine,
Lupine to Porcine,
Canine to Feline,
Arachnid to Lupine,
Canine to Porcine,
Lupine to Bovine and
Arachnid to Feline
is simply 0.
0 miles.

You stated "No other pairs are connected by roads."
The pairs given in the question with the difference in miles attached are:
Arachnid to Canine,
Bovine to Lupine,
Feline to Porcine,
Lupine to Canine,
Bovine to Porcine,
Bovine to Canine,
Porcine to Arachnid and
Feline to Lupine.
The pairs for which we're to find the distance between aren't included in the pairs whose difference in distance are given. That means the latter pairs aren't connected by row, hence do not have any difference in distance by road; 0 miles.
 
First, I tried sketching it out, but that obviously was going to be too difficult (or far too time-consuming). Therefore, I made six columns, labeling them the six groups: Arachnid, Feline, Canine, Lupine, Bovine, and Porcine. Then I went through the paragraph with the distances and under each column I would write which connected to which and the distance. This sheet looked as:

Arachnid-Canine (15), Porcine (1)
Feline-Porcine (6), Lupine (11)
Canine-Arachnid (15), Lupine (3), Bovine (7)
Lupine-Bovine (12), Canine (3), Feline (11)
Bovine-Lupine (12), Porcine (9), Canine (7)
Porcine-Feline (6), Bovine (9), Arachnid (1)

From here, I started calculating the shortest difference. Basically, I took the two camps and wrote it out as stated. Then I took the possible paths from the first camp, including the distance to the next possible path. I proceeded to do this to get to the camp we were looking for. Basically, I did all possible combinations, and went with the shortest one. The asterisks are where I felt it unnecessary to continue the scenario. It is as follows, as I’m sure the work explains it better than I did;

Feline to Bovine
Shortest Distance is: Feline to Porcine to Bovine
Porcine (6) + Bovine (9) = 15
Lupine (11) + Bovine (12) = 23

Lupine to Porcine
Shortest Distance is: Lupine to Feline to Porcine
Bovine (12) + Porcine (9) = 21
Canine (3) + Arachnid (15) + Porcine (1) = 19
Canine (3) + Lupine (3) + Bovine (12) + Porcine (9) = 27
*Canine (3) + Lupine (3) + Canine = did not finish, goes back to Canine and definitely would not be the shortest route
Canine (3) + Lupine (3) + Feline (11) + Porcine (6) = 23
Canine (3) + Bovine (7) + Porcine (9) = 19
Feline (11) + Porcine (6) = 17

Canine to Feline
Shortest Distance is: Canine to Lupine to Feline
*Arachnid (15) + Canine (15) + () =already over the lupine/feline route distance
*Arachnid (15) + Porcine (1) + () =already over the lupine/feline route distance
Lupine (3) + Feline (11) = 14
*Bovine (7) + Lupine (12) + () = already over the lupine/feline route distance
*Bovine (7) + Porcine (9) + () = already over the lupine/feline route distance
*Bovine (7) + Canine (7) + () = already over the lupine/feline route distance

Arachnid to Lupine
Shortest Distance is: both the [Arachnid to Canine to Lupine] and the [Arachnid to Porcine to Feline to Lupine] are the same distance (18)
Canine (15) + Lupine (3) =18
Porcine (1) + Feline (6) + Lupine (11) =18
Porcine (1) + Bovine (9) + Lupine (12) =22
*Porcine (1) + Arachnid (1) + () =will be over the route distance

Canine to Porcine
Shortest Distance is: both the [Canine to Arachnid to Porcine] and the [Canine to Bovine to Porcine] are the same distance (16)
Arachnid (15) + Porcine (1) = 16
*Lupine (3) + Bovine (12) + () =will equal more than the Canine to Bovine to etc. route
*Lupine (3) + Canine (3) + Arachnid (15) + () =Equals more than the shortest distance
*Lupine (3) + Canine (3) + Lupine (3) + () =will equal more because it goes back to Lupine
Lupine (3) + Canine (3) + Bovine (7) + Porcine (9) =22
Lupine (3) + Feline (11) + Porcine (6) =20
Bovine (7) + Porcine (9) =16

Lupine to Bovine
Shortest Distance is: Lupine to Canine to Bovine
Bovine (12) = 12
Canine (3) + Bovine (7) =10
*Feline (11) + Porcine (6) =will equal more than the shortest distance

Arachnid to Feline
Shortest Distance is: Arachnid to Porcine to Feline
*Canine (15) + Arachnid (15) + () =will equal more than the shortest distance
*Canine (15) + Lupine (3) + () = will equal more than the shortest distance
*Canine (15) + Bovine (7) + () = will equal more than the shortest distance
Porcine (1) + Feline (6) =7

It took me a while to figure this out-probably half an hour. There is probably a much quicker way, but this worked for me and I am fairly certain that it is correct. I am not very good at math and writing it all out seems to help. I did cut a few corners by using asterisks when I knew that an equation was not going to be the shortest distance.
 
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