Final answer:
Duty-based reasoning dictates that the nurse should prioritize the needs of the patients and agree to work the overtime, as this is the higher moral duty in the scenario presented.
Step-by-step explanation:
In the scenario where a nurse is reluctant to work overtime due to a social commitment but three nurses have called in sick, duty-based reasoning would suggest that the nurse should consider the needs of the patients and agree to work overtime. This follows the principle that higher duties, such as providing essential healthcare, generally take precedence over personal commitments.
As in the example provided with the coworker experiencing chest pains, one has a prima facie duty to fulfill promises, but this is overridden by the more urgent moral duty to render aid in an emergency. The nurse's responsibility to the patients, who require care and may suffer without adequate staffing, is deemed an actual duty in this context.
This resolution reflects the professional commitment to patient care that is expected in healthcare work. If possible, the nurse may seek to find a compromise, such as finding a replacement, but the prompt care and well-being of the patients is the utmost priority according to duty-based ethics.