This is why I don't ride on paths, unless it's a very off -peak time.
If i hear on your left, I hold my line and let the person pass. In the regular places I ride right around my house, I usually "hear" the bike before they say it, and not everyone says it.
If I am passing I say, "Bike passing on your left."
Today I had a first time experience with a woman rider. I was riding with my friend who is much slower than me. When we got to a flat. straight a way, I took off. She knows I will stop and wait. So a much younger woman came up behind me and passed, when I was going around 17. I may have slowed momentarily to fix something. She did not announce herself! I figured, well she was rude, even though I said hi to her, so I got in behind her. Usually, I ask if it's OK. She wasn't going any faster than me. I followed her for 2-3 miles at 16-21 mph and was on her wheel. Finally I pulled over and said, "Thanks, i am going to wait for my friend."
She replied,"Oh, I didn't even know you were there..." Yeah, right. She thought she had dropped me, but there is no way she couldn't hear me.