Final answer:
While Maria and Sydney did the same amount of work climbing the stairs, Sydney displayed greater power by completing the climb in a shorter amount of time.
Step-by-step explanation:
The question involves comparing the amount of work and power done by Maria and Sydney as they climb a flight of stairs. Since Maria and Sydney have the same weight and climb the same flight of stairs, the work done by both is the same. Work (W) is calculated as the product of force (F) and distance (d), and in this case, the force is the force due to gravity, which is equivalent to their weight.
However, the power generated by each is different because power is the rate at which work is done, and is defined as work done over time (P = W/t). Maria takes 3.2 seconds to climb the stairs, and Sydney does it in 3.0 seconds. Therefore, Sydney has a higher power output than Maria because she did the same work in less time, resulting in a smaller denominator in the power formula. Although both performed the same amount of work, Sydney demonstrated greater power due to the quicker completion of the task.