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As is often the case in a power problem, the best strategy is to first calculate the work done; then use the work done and the time to calculate the power. See the two equations in the Formula Frenzy section.
The difficulty in this problem pertains to the absence of a stated value for the force applied by the mountain climber. If a climber is ascending a mountain (usually at a slow constant speed), then the applied force required to sustain the motion is equal to the weight of the climber. So in calculating the work done by the climber, assume a constant speed motion and use the weight of the climber. See the Formula Frenzy section.
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