Final answer:
Option C is correct, as machine X is 3 times more powerful than machine Y, it does the same work in 1/3 the time. This relates to the concept of power in physics, which is the rate at which work is done.
Step-by-step explanation:
When comparing the power of machines X and Y, where machine X is 3 times more powerful than machine Y, the correct statement is option C: Machine X does the same amount of work in 1/3 the time it takes machine Y. This is true because power is the rate of doing work, or the amount of work done per unit time. If machine X is 3 times more powerful, it can either do 3 times as much work as machine Y in the same time, or the same amount of work in 1/3 the time. Therefore, statements A and B are incorrect.
Understanding the relationship between work, power, and time is important when analyzing production technology. The choice of production technology often depends on the cost efficiency and power required for certain tasks. Efficiency measures the ratio of output work to input work and is significant in practical applications, as no machine is 100 percent efficient due to factors like friction causing some of the input work to be converted to heat energy.