How to deal with jealous/ passive-aggressive coworker?

Hello! So I just started this new position. Long story short I work with this much older woman and she acts slightly jealous of me. I started this job 3 weeks ago and I almost learned everything so far. I get my work done quite fast, and she is often behind.

She tries not to teach me more because she thinks I will “get overwhelmed” but I explained that I was not overwhelmed, and I am happy to learn anything. She seemed to get a little bit pissy that I said that. She will also get snappy towards me when she sees I have finished my duties before her, and even once was upset that I had came up with idea to make our work easier. I am NOT trying to be apart of this drama :( she told me today that she acts this way because she “no longer feels needed”..

I don't know. I’m just trying to get my work done quick, and go home on time. I don't know what to do. Do I work slower to avoid problems? Talk to a manager?
How to deal with jealous/ passive-aggressive coworker?
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