To analyze the situation, we need to consider the definitions of work and power.
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Work: Work is defined as the energy transferred when an object is moved over a distance by an external force. In this case, since both the student and the friend are walking up the same hill, they are both doing the same amount of work against gravity (assuming they start and finish at the same height).
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Power: Power is the rate at which work is done, defined as work done per unit of time. The formula for power (P) is: \[ P = \frac{W}{t} \] where \( W \) is work and \( t \) is time.
Given that the friend completes the journey in less time, we can conclude that:
- The work done by both the student and the friend is the same since they both walk up the same hill and have the same mass.
- The time taken by the friend is less than the time taken by the student.
Thus, the friend's power must be greater because they are doing the same amount of work in a shorter period.
Therefore, the true statement about the situation is:
The power of the friend is greater than the power of the student.