Answer
The force of the rope does $900~J$ of work on the skier.
Work Step by Step
When the speed is constant, the force of the rope on the skier must be equal in magnitude to the component of the gravitational force opposing the skier's motion.
Since the speed is constant, either $v = 1.0~m/s$ or $v = 2.0~m/s$, in both cases, the force $F$ must be the same in both cases.
Therefore, the force of the rope still does $900~J$ of work on the skier since the distance of $8.0~m$ is the same in both cases.
