Rate Determining Step: Explained & Contradicted

[SuccessTheory]

If a slow elementary reaction between two colliding species takes 2 s, and a fast step afterwards takes 1 s the total time is 3 s. Since the time for the overall reaction's completion is increased by the fast step, why is it ignored in determining the rate law? Thanks,

P.S. This is not a homework question, this is an example I thought of that seems to contradict the use of the rate determining step.

 

[Char. Limit]

Because the faster step depends on the slower step.

The faster step will consume the products of the slower step faster than new products are being made. Because of this, the faster step has no real effect on the rate.