Fill a gap between concrete to floorboard

[Surftuzzer]

Hi

Wondering what to use for this gap. Needs to be level and smooth but not fussed re appearance as under a rug.

The photo shows a gap between floorboard trim and old concrete hearth edge. The floorboard trim is tatty and slopes down - so we need to cover the wood trim and make level with the concrete so it’s smooth for the rug to lay over it without a dip/bump.

Our actual slate hearth is further back (less big than the concrete you see here), so there’s no fireplace concerns. The spot might get stood on but isn’t a walkway as such.
Any tips? Wood filler? Levelling compound?

 

[fillyboy]

two part wood filler, the type you add a hardener to. Sets rock hard and bonds well.

https://www.screwfix.com/p/ronseal-high-performance-wood-filler-natural-550g/51811?msockid=3e04eb06897b69970a25f8f0889b68e0

Levelling compound would work as well but may be liable to break up if not deep enough.

 

[motorbiking]

It looks like it's been previously filled, but traffic has caused it to crack and fall off/out. I'd be tempted with a sealant/mastic to give it some flexibility

 

[Surftuzzer]

two part wood filler, the type you add a hardener to. Sets rock hard and bonds well.

https://www.screwfix.com/p/ronseal-high-performance-wood-filler-natural-550g/51811?msockid=3e04eb06897b69970a25f8f0889b68e0

Levelling compound would work as well but may be liable to break up if not deep enough.

Used this and was just the ticket.