Imagine that you and your friend (of equal size and weight) are competing in competition to see
who can run up ten flights of stairs faster. It takes you
100 seconds to run up the ten flights of stairs, but it
takes your friend 120 seconds. Who did the most work?
Who exerted the most power? Explain your answer.

1) The work done by both friends are equal

2) The first friend exerts the most power

Explanation:

1) The given parameters from the question are;

The size and weight of one friend = The size and weight of the other friend = W

The distance ran in the upwards direction = 10 flights of stairs

The work done = The weight × Distance

The work done by one friend = W × 10 flights of stairs

The work done by the other friend = W × 10 flights of stairs

Therefore, the work done by both friends are equal

2) The power exerted = The rate of doing work = Work done/(Time taken to do the work)

The power exerted by the first friend = W × 10 flights of stairs/(100 seconds)

The power exerted by the other friend = W × 10 flights of stairs/(120 seconds)

W × 10 flights of stairs/(100 seconds) > W × 10 flights of stairs/(120 seconds)

∴ The power exerted by the first friend > The power exerted by the other friend

The first friend exerts the most power