The tendentious answer on philosophy is an invitation for what would be another "Dabblers and Blowhards" drive-by shooting. It's not enormously surprising that this question is 'rarely asked'. One would learn a lot more about philosophy ("what questions are these guys asking?" "what are some of the answers they've come to?") from even a mediocre introductory text or a chat with a TA/tutor, than by assuming that this…
It's hard to get that deep in a couple paragraphs. But there is a longer version here: http://paulgraham.com/philosophy.html
Suppose that my mother has Alzheimer's disease, and that I find the prospect of caring for her inconvenient, undesirable, and/or expensive. Do I have a responsibility to care for her anyway?
It is "useful" because it could potentially describe a real-life situation in which one might have to make a decision. Analyzing this quickly leads one to a general discussion of ethics.
As you point out, definitions are imprecise. What does it mean to say I have a "responsibility", or that I "ought" to do something? Logic and observation can get one to "If I do nothing, then my mother will suffer and/or die", but this is not the heart of the matter.
I think there is no hope of a "solution", in the same way, say, that Fermat's Last Theorem was proved. But does that mean that studying ethics, and what the usual lineup of dead white males had to say about it, isn't worthwhile?