It does not work that way. If you correct the problem which caused LTFT to be in +10%; your STFT will immediately go to -10% and then both will go slowly towards 0. The actual fuel provided by ECM is the sum of STFT and LTFT.
The time delay will depend upon manufacturer but the "slow" is with respect to the oscilloscope! If your engine is in that "cell" for a minute or so, it LTFT will definitely be back to normal.
Since you are asking this questions, I am assuming you are familiar with the basics and I am not explaining the "cell" concept.
Few Key ideas in understanding fuel trims:-
- There is no single STFT/LTFT value
- Engine has lots and lots of STFT and LTFT based upon different operating conditions.
- Regardless of lean or rich as indicated by trim, the ECM is always trying to keep the engine running in the stoich mode (except when it is not!)
- Since there are lots of cells, you could get both rich and lean codes and will drive your brain in to somersault!
- When it hits the pre-programmed limit, it lights up the code
scannerdanner and schroidingercats are two youtube channel that you want to subscribe to if you are interested in understanding this.
Short answer "a minute or two"