Final answer:
When the time required to perform a given amount of work decreases, the power developed increases because power is the rate of doing work, which is work divided by time.
Step-by-step explanation:
As the time required to do a given quantity of work decreases, the power developed increases. Power is calculated by dividing the work done by the time it took to do the work (W/P = t), and it is the rate at which work is done. As such, if an amount of work is done in a shorter amount of time, this means there's a higher rate, thus more power. A simple example is when lifting weights; if you lift the same weight to the same height more quickly, you are increasing the power you exert.
Everyday appliances and machines are rated in terms of power. This concept helps us understand their energy consumption rate regardless of how long they are operated. The term commonly known is watt (W), which can relate to any form of energy or work, not just electricity. Multiplying power by time yields the energy consumed, hence why electricity is sold in kilowatt-hours.
Therefore, when we increase power, we are either increasing the amount W of work done or decreasing the time t. If the work remains constant and the time decreases, the only way to balance the equation P = W/t is for the power P to increase.