Time management and organization often require a team effort. Remember to keep your co-workers in the loop. There are few things more annoying than asking someone to do something, not get a response, ask again, not get a response, then, two weeks later, you get a reply telling you it’ll be done next week.
If you get a request, reply to it, asap. If it’s not going to get done until next week that’s fine. As long as you answer. It’ll save your co-workers a lot of grief.