How did Carpathia find Titanic's lifeboats

This may or may not be a dumb question. It does not seem to have been addressed elsewhere, to judge from a not exhaustive search in the most likely threads.

We know that Boxhall's estimate of Titanic's position was out by a bit (13 miles too west?). We know that Alicia Coors has taken exception to this egregious navigation error. How did Carpathia manage to steam straight to the lifeboats in her famous early morning race through the dark? I've never read of her having any difficulty finding Titanic's boats, yet if she was making for a spot >10 miles from where they actually were, then she surely ought to have turned up at dawn in an empty sea? Those with sea experience can guide me on the practicality of spotting a lifeboat at such a range, even from a ship's bridge. I would have thought it difficult.

So what's the story? This does not appear to be a widely discussed/wrangled over/bickered over/snarled over point.

Also, the widely quoted distance of 57 miles from Carpathia's receipt of the mayday to reach Boxhall's estimated position must be in error, since Boxhall was in error (as Alicia will no doubt remind us). Can we arrive at the correct distance, having hindsight (granted Carpathia's own position may have been incorrect - but she didn't sink and mark her spot forever, so Alicia can't accuse Rostron of incompetent navigation).
So Rostron was probably not where he thought he was... hmm, what will Alecia have to say about that?

Had the sea become rougher by the time Carpathia reached the boats? Rostron had no trouble (that we know of) avoiding icebergs. Had they become more visible due to a chop having got up?
Rostron DID have to avoid icebergs on his run to
Titanic - he reported having to go around a number of them.

Yes, the sea got rougher in the morning.

Was anybody really where they thought they were? Who can tell?
>>So Rostron was probably not where he thought he was<<

He wouldn't be the only one. Navigation in that day was not the sort of exact down to the last inch affair that we tend to expect these days. (Thank you very much, GPS!) All in all, they did managed extremely well with star tables, chronometers, sextants, and the like, but there were variables at work that they had to make a "best guess" at.

>>...what will Alecia have to say about that? <<

What does it matter?
Here is another question. (It might be a dumb question, too.)

Did the lookouts on the Carpathia see the Titanic's lifeboats before those in the lifeboats saw the Carpathia ?