[attachment=0]spider_fly.gif[/attachment]
This was my first run at it…
…but didn’t check the math.
starting at spider point go 6 ft to the left straight across 30 feet wall then diagonally from 30 ft wall to fly.
kool problem… maybe I should start a math problem sticky!
Excellent approach James. There is a shorter path.
That would be over 42 ft. It would be shorter to just go straight down over and back up (42 ft). 
48.5…
It kind of makes me wonder what a common spider would actually do.
I actually agree with James’ solution.
There are three obvious paths:
Other than those three paths, I don’t think there is anything even a-priori considerable as a possible fastest path – of all possible unfoldings of the cube, those are the only 3 straight lines (well, there are other straight lines, but they’re just the inverse of the lines drawn so they’re necessarily equal in length and need not be considered separately).
This is what I think, of course, but I could be wrong.
So, let’s start with the most obvious path, path red. Here is what it looks like with the cube unfolded, measurements provided:
Next most obvious path to me was the green one, this is the one I tried first. Here is what it looks like unfolded, measurements provided (imagine, instead of folding the two ends down and keeping them connected to the bottom rectangle, you’re folding them towards yourself and keeping them connected to the side rectangle):
We don’t even have to do the math on this one – if you know any geometry, you know that the hypotenuse of a triangle must be greater than the triangle’s greatest side – this triangle’s greatest side is already 42, so the entire green path is by necessity longer than the red path above (the actual green path length is 43.1741 in case you’re wondering).
So now for the final (in my estimation) possible path. With this unfolding, imagine unfolding the right end keeping it connected to the side closest to you, the viewer (as in the above example), and then unfolding the bottom side downward (ending up in the position of the bottom middle rectangle in the pic below), and unfolding the left end keeping it connected to the bottom rectangle:
I think we have a winner!
I actually thought the solution was what James thought on first impressions, his solution is intuitively what I thought would work although I am not sure why. There are actually a vast amount of solutions in 3D albeit a limited version of it, well done flannel, seems I got here too late. Although if there is a shorter solution I should probably think on. 
I think a shorter solution will come from traveling along the other wall, although this seems intuitively illogical. It might also be that contrary to what you would imagine using the ceiling is better. I think you have to remember that the actual solution will be an actual zigzag using many walls, although I don’t have time to work out all the possible solutions and what is shortest,.
Although keeping the relative angles at their minimum obviously seems a key to the problem.
There is one more option left out from FJ’s list, if you move the first blue corner down to the bottom and the last corner up onto the front edge, but it ends up to be about 47.5 in length. Through symmetry, I think that covers all possible options (assuming no teleport devices handy).
@james I also discovered that option a bit later, but didn’t edit my post to include it because it was actually quite a bit longer a path than the other ones.
We’ve covered all of the unfold-cube-make-straight-path options, I think, once we’ve considered that one. I’m very inclined to think that the answer is necessarily a straight path between the points on an unfolded cube.
the obvious answer is to wait until the fly comes closer
If that’s the answer I’m going to jump out of a window.
the 40ft one is the right answer
Answer for shortest distance:
[tab]The shortest path is 40 ft.[/tab]
Answer diagram:
[tab][attachment=1]SpiderandFly_600.gif[/attachment][/tab]
Comparison of solutions:
[tab][attachment=0]spider-and-the-fly-solution.jpg[/attachment][/tab]
of course
I was looking for a solution like that. I had unfolded it a number of different ways, idk why I didn’t think of that.
Aaaakkk… haha… using the top AND bottom… making a perfect spiral.
…got us… o well.
Btw, the way to resolve this sort of problem to KNOW that you have the best solution possible is to merely go through the entire truth table. Take the first side where the spider is from which you have 4 sides. Each of those sides leads to 3 other edges that lead to 3 more until you finally get to the fly. It is tedious, but it guarantees all possible solutions have been examined.
one other conceptual trick for this particular type of problem (unfolding cubes) is that you can ‘roll’ one unfolded side up or down the diagram. If you look at my last diagram, the difference between that unfolding and the solution unfolding is that the right edge was rolled (up and counter-clockwise) up one edge.