Hot and timely research problem with a slow student I am a postdoc and currently co-supervising a novel PhD student who works very very slow and needs to be spoon-fed most of the time (which is reasonable considering she's in early stages of her PhD). We are working on a very hot topic and have defined a research problem to work on. She has been working on it for 2 months, but I'm afraid we are going to miss out on publication due to her slow pace. I, however, can see where the work is going and can do it on my own very quickly and maybe get it published right way. This work is an incremental research on something I did before, but for the student to climb the learning curve, it will take a considerable time.

Thinking about this, I have two options:


Let her take her time and do research as any usual PhD student but
push her to be quicker (not sure how). 
Do the research work myself and get it published much sooner than pursuing option 1 above, and list her as a co-author.


Now option 1 gives the student a fair-go in risk of missing out to another research group that may be doing similar research. Even under this option, I'm not sure if the student will really do a fantastic job eventually. 
Option 2 seems unethical to me because a student should have his/her time to learn and experiment, but will allow her to learn the publication process and contribute to the production of the paper.

What do you think I should do?
If you have taken on the responsibility of shepherding this student to her doctorate then you have an ethical constraint that overwhelms most other considerations. The only exception to that, that I can see, is if the research is actually life saving in some way. 

I a lot of supervisor-supervisee relationships the advisor can do the work on her/his own without the student. But that doesn't ever imply that the student should be left behind. The supervisor has more experience in field and in research in nearly all cases, so the student requiring a (possibly long) learning curve is pretty typical. 

The "hotness" of the research topic doesn't change your ethical responsibilities. If you don't want to honor that you shouldn't take on advisor roles. 

However as aeismail suggests, the student needs a suitable problem, not necessarily this problem. If she is at the beginning of the process it might be reasonable to morph her participation into a different problem. 

But, your assessment of her overall ability may also be wrong. She may, in fact, have a breakthrough moment in which things fall into place. And if the problem is that she lacks key background elements for some reason, you could make it go faster by finding ways for her to quickly come up to speed on those. 

Finally, it isn't uncommon in many fields, including mathematics, for an advisor to give some hints to the student, pointing out the direction to be explored, if not more.