Concerning the growth of grass

Hello- this is my first post here. I checked the tags before-hand, so I think I'm okay.

Setting: Japan in the 1600's, though I'm not sure it matters.
Search terms: I've searched for grass, growth of grass, grass hardiness, and other variations thereof. All the sites I found about grass simply gave instructions about how to plant and cultivate grass. Wikipedia was no help either.

My question is this- how long would it take for a dirt footpath to grow over with grass? My plot has something to do with time travel, and assumes that a path would have to be be decently hidden from view after fifty years or so. If anyone could help me out, or at least point me towards a helpful site, that would be great.

Edit: I believe I have a sufficient answer- thank you all so much for your help!