Astronauts on a tether Recently, I went to a competition with a science test. One of the questions was as follows:

Two astronauts (A and B) are tethered together in space. Simultaneously, Astronaut A pulls on the tether with 20 lbs. of force, and Astronaut B pulls on the tether with 8 lbs. of force. What happens with to the astronauts?
A. Nothing.
  B. They are pulled together with 28 lbs. of force.
  C. They are pulled together with 12 lbs. of force.
  D. (Can't remember what this answer was)
  E. Cannot determine without the astronauts' masses.

Apparently, the correct answer is apparently C, but I kept getting 32 lbs. towards each other:
There are four forces to consider.
1 <--|--> 2   3 <--|--> 4
   A-|-------------|-B

Forces 1 and 2 are resulted from A's tug and the opposite reaction to his tug; same for 3 and 4 but for B's tug. Therefore, we have the following forces:
20-->|<--20   8 -->|<-- 8
   A-|-------------|-B

|____|_____________|____|
   X        Y        Z 

Segment $X$ goes to the right with 20 lbs. of force, segment $Y$ goes to the left with 12 lbs. of force, and segment $Z$ goes to the left with 8 lbs. of force. So we have:
20-->|    <-- 12   |<-- 8
   A-|-------------|-B

|____|_____________|____|
   X        Y        Z 

So the force in segment $Y$ "overrides" the force in segment $Z$. So we have:
20-->|    <-- 12
   A-|---------------B

|____|__________________|
   X          YZ 

I thus conclude that they are pulled together with 32 lbs. of force.
a. What did I do wrong in my solution?
b. How do I get 12 lbs.?
 A: Let me start out by saying this: subtracting the forces is certainly wrong. I have no idea why they would get the answer 20-8=12, other than wanting to subtract 20 and 8 and looking for an excuse (not exactly likely). A quick though experiment confirms what I say. If you extend their logic, then if both astronauts pulled at 20 lbs of force, then they wouldn't move at all, which is certainly wrong.
I propose looking from the point of view of a point in the center of the rope. From the perspective of that point, astronaut 1 pulls accelerates himself with 20 lbs of force towards the point. From the perspective of the point, astronaut 2 accelerates himself with 8 lbs of force towards the point. Therefore, they head towards each other with 28lbs of force.
Please explain down votes, so I can edit the post to fit the criticisms.
A: If Astronaut A were pulling with 20 lb of force then Astronaut B should be feeling 20 lb of force if he were just holding the line. If he is only "pulling" or "feeling" with 8 lb of force ,then he's actually letting the line slip through his gloves while using sliding friction to maintain 8 lb. of force. An insidiously tricky question if you ask me (and I'm not sure this is makes physical sense.) The tether should have a single vector of "force" or tension transmitted or shared in both directions.
A: Consider the frame of reference of the rope:
Astronaut A pulls on the rope with $20 \text{ lb-f}$, so by Newton's Third Law, the rope pulls on Astronaut A with the same force.  There are no other forces acting on Astronaut A.  Therefore,  Astronaut A will accelerate along the rope with an acceleration appropriate to this force and his mass.
Similarly, Astronaut B pulls on the rope with $8 \text{ lb-f}$, so by Newton's Third Law, the rope pulls on Astronaut B with the same force. There are no other forces acting on Astronaut B.  Therefore, Astronaut B will accelerate along the rope with an acceleration appropriate to this force and her mass.
The rope itself will accelerate in the direction of Astronaut A, with an acceleration appropriate to its mass and a force of  $12 \text{ lb-f}$
A: The existing answers are good, but i try to present an answer that encompasses all the concepts together.
Step 1: Consider the astronaut B and the rope to be a system, and the astronaut A to be the other system. The astronaut A applies a force of $20 \text{ lb-f}$ on the other system, and hence, by Newton's Third Law, the other system applies a force of $20 \text{ lb-f}$ on the astronaut A system, towards the center of the rope.
Step 2: Applying similar reasoning to astronaut B, we find that the astronaut B experiences a force $8 \text{ lb-f}$ towards the center of the rope.
Bonus Step 3: Consider the rope to be a system. It has two forces acting on it, $20 \text{ lb-f}$ towards astronaut A and $8 \text{ lb-f}$ towards astronaut B. It experiences a net force of $12 \text{ lb-f}$ towards astronaut A.
Physical Interpretation
The astronaut A would see the astronaut B coming towards him, and the rope collecting behind him. On the other hand, astronaut B would see the astronaut A coming towards him, but the rope would be slipping out of his hands, towards A. The tugging force by the rope at the tethering point on the astronaut B (along with a little friction at the rope) would be the force actually pulling the astronaut B.
Also, in reality, no person can apply a continous constant force, but like a boatman, has to pull at intervals. So the rope can momentarily collect even near B, but would be soon pulled back by the greater force by A.
Finally, the (hypothetical) answer to the science test question:

(C) Astronaut A is pulled by 20 lbs. force and astronaut B is pulled by 8 lbs. force, both towards each other

A: Let's suppose first that the astronauts are tethered by a rope to their suits, and the rope is tight, in that initially there is no slack. Put another way, the length of the rope is the distance between them.
They both grab the rope and pull with their respective forces and keep holding those points on the rope. 
Now astronaut A pulls with 20lbs of force so he moves with 20 pounds of force toward B and the rope (with some slack on his side) towards A with the same force.
Now B pulls with 8lbs of force so the same applies as above, some slack, but now the rope has a net force force of 12lbs toward A and so moves toward A.
But B is holding the rope so the tension in the rope, a net 12lbs also pulls B toward A.
So B moves toward A with 20lbs of force (8+12),
A moves toward B with 20lbs of force.
Does that make sense?
If by 'pulled together' it means the net force on the rope, then you get 12lbs as your answer.
