At one point you’re going to work on a team where you don’t feel that a team member is pulling equal weight. It is truly the responsibility of the project manager to ensure fairness across team responsibility and accountability.

Project Team Member
I don’t know the position you are applying for that prompted this question, but if it is to be on a project team (not the manager) then I would answer this carefully because it is a behavioral skill the interviewer is looking to identify. The best approach to this is to answer by saying that you are always conscientious about meeting or exceeding project expectations. Tell the interviewer that you provide comprehensive project updates and clearly document any time your progress is impeded. Clearly documenting impediments in your regular project update without an attacking tone (when applicable) would put any slow team member in the spotlight. A good project manager would manage that team member accordingly. Try to keep the answer to this question as short as possible, but clearly stating you focus on doing the best job possible and you let management work on any team performance issues.

Project Manager
Simple Answer: As the project manager, you would work with the slower team member to identify daily goals and discuss consequences if goals aren’t met. It would be important to make sure the team member understands and agrees to the daily goals AND the consequences of not meeting those goals.

More Complex Answer: As a project manager I ensure all team members are meeting performance expectations by using a Scrum project management framework. Scrum project management is a framework that has been used from simple projects to changing the way an entire enterprise does business. Scrum significantly increases productivity and reduces time it takes to achieve business value by identifying obstacles early and managing them appropriately.

Scrum PM isn’t complex, but at its core are daily, standing meetings that last no more than 15 minutes. Each team member is asked 3 questions.

1. What did you accomplish since we last meet?
2. What will you accomplish before we meet next?
3. Did you encounter any obstacles?

For the first question above, if accomplishments weren’t inline with what was expected based on the previous meeting then an offline conversation should occur between PM and team member. If the inability to reach daily expectations becomes routine by one particular team member it becomes clear who is negatively impacting the speed of the project (reference ‘simple answer’ above at this point).

Note:
If daily Scrum meetings aren’t conducive for a particular project, a similar weekly (or monthly) meeting can be held to discover if expectations are being met.

I want to clarify a sentence I wrote above:

"Clearly documenting impediments in your regular project update without an attacking tone (when applicable) would put any slow team member in the spotlight."

I didn't mean for this sentence to sound like it is OK to write in an attacking tone. I meant that you only mention a slow team member's performance as an impediment ("when applicable") - there are plenty of project impediments that aren't caused by a slower team member. In addition, never write or state your project impediment in an attacking tone.