Answering questions isn't the only way to earn rep. You can also earn rep through asking good, well thought out questions and by suggesting edits (one example of a user that clearly isn't going for the fastest gun). Neither of these are particularly time critical tasks (it's easier to get an edit approved if somebody is about to look at it, but generally there isn't a significant delay in edit approvals, if the edits are worthwhile).
Looking back at your reputation activity, you seem to have had rather mixed results with the questions you've asked, attracting a fair proportion of down votes. I’d suggest that rather than chasing the fastest gun prize, where you’re clearly at a disadvantage, you should concentrate on maximising the benefit of your interactions. Take time to read your questions before you submit them and think about whether or not the question contains enough information that you would be able to understand it, without any additional context. Consider using something with a built in spelling and grammar checker, to prepare your questions and minimize your mistakes. Take time to format them correctly etc, etc... It just occurred to me I could have just told you to go read the John Skeet blog post :)
If you want to answer questions, browse the unanswered questions in your area of expertise. If you can answer some, great, take your time and produce a good answer. If the question needs improved to make it clearer, then suggest some improvements and see if they get approved. If they do, then you may also get an up-vote on your answer from the 10K+ users that tend to approve older post edits.
Essentially, if you're not going to be the fastest, make sure what you add is of good quality. If you do get the chance to be the fastest, make sure you use that time to ensure you're not only first, but you're the best answer...
Slightly off topic for your original question, but I noticed two other things about your SO profile, which surprised me.
1) You don’t have any favourites. When I’m browsing the site from my mobile, I usually do it to read questions / answers, voting as I go and adding favourites if there’s a reason to go back to the post. It could be I’m interested in seeing how it turns out, or it could be that I think I could add an answer when I get to a keyboard. If you use the tools that are provided, you can maximise the benefit of those times when you’re not on a mobile interface.
2) Despite having asked 14 questions, you have only ever cast 12 votes. As I said, I do a lot of voting from my mobile (usually on questions), so I’m surprised your vote count is so low. If everybody had the same approach, then it would be very difficult for anybody to gain rep. If you find the site useful, then perhaps you should consider other ways that you can give back as well.