Your choice: You can try to circumnavigate this person so that the quality of your work doesn't suffer as a result of their lack of competence. Or, if you're truly hitting the wall, you can do what some people I know who have worked with incompetent people have done: They changed jobs.
The entitled lifestyler
Notwithstanding the recession, this person, like my friend's "princess" staffer, follows job requirements to the letter, and no more, puts in exactly 40 hours, no matter what, constantly talks about work-life balance, and acts like there is a labour shortage even while their organization is downsizing.
And then, while you wonder what planet they think they inhabit, they complain about not being promoted.

Work-life balance is one thing, but oblivious feelings of entitlement are another. The dirty truth about contemporary corporate life: Notwithstanding every organization's chatter about work-life balance, if someone wants to get ahead, they need to be seen working. Walking out the door at 5 doesn't cut it.
The other rule: You need to do exceptional work, which goes well beyond job expectations and visibly contributes to team effectiveness.
If you are a boss, you need to spell out those rules of promotion.
If you are a co-worker feeling like you are pulling too much weight to cover for an entitled lifestyler, be respectfully assertive about what you are, and are not, prepared to do.
You also need to understand other people may have personal lives that are much more complicated than yours.
Rather than assume it's up to you to pick up the slack, or attack your co-worker about burdening you with an excessive workload, see if you can help educate or negotiate with the boss about work demands.
So what do you do if you've tried everything, and quitting isn't an option? Hold your nose. Sometimes we just have to live with people who we find problematic.
And remember: If you think someone just doesn't get it, there is a pretty good chance they or someone else you work with is saying the same thing about you.
Barbara Moses, PhD, is a speaker, organizational career management expert and author. A revised and updated version of her book What Next? Find the Work That's Right For You is now available.
