I suggest you comparego through with her and compare what you would have done to complete the task with what she did, step by step, just this time and a few times in the future for different types of tasks.
I would make it clear how puzzling it is that she took so much longer and that you want to bring her to the level that is needed to be a respected co-worker.
SimilarilySimilarly, reflect to her how inappropriate it is to imply being bored and surfing the web during working hours. On the other hand, being honest and open is valueablevaluable, so I suggest to show her outlets like surfing in working breaks, being bored after she completed the task or finding out why she is bored while she has a task.
After a few days I hope you'll get a feeling for whether she integrates your advice into her habits. Because if she does not, she is wasting your time.