This is a forum for robotics. And this circuit has nothing to do with it. I tried to help this time but it will be last. Next time I will try to solve only something directly related with robotics.

Does this problem mention anything else the resistance of the AB cable or tell the value of some current?

In my "solution" you must consider the resistance of the cable AB and make use of the formula R=p*L/S(otherwise the position p would be meanless). Then you can get the the resistance for the segments AX and XB are proportional and are a function of d. In other words:

rAX+rXB=(p/S)*50 for the whole cable

rAX=(p/S)*d for the segment AX (p is the resistivity and S the area of the cable)

we dont need the formula for segment XB because it is not linear independent from the first two.

By fusing both formulas we will get:

rAX=rXB*d/49 [1]

By using Kirchoff's laws you will get that : 1) iAX = iXG + iXB[2] (iAX is the current in the segment AX, iXG the current in the segment X ground and so on)

2) 160 = iAX*rAX+iXB*rXB[3] and 200 = iAX*rAX+iXG*R[4]

[1][2][3][4] are all the linear independent equations I can think of and they are only 4, on the other hand we have iAX, rAX, rXB, iXB, iXG, R, and d which are 7 variables. This means that this system has infinity number of solutions, you just cant solve it. Unless, if are suppose to leave some values as letters, but I don't believe because if they wanted so they would not have supplied the values for the potentials and so on.

I believe if I were a worker at this company I would know the resistance of the cable AB and I would have a multimeter so I would measure the current in AX and in XB. that would kill 3 variables and I would have and system with 4 equations and 4 variables.