increasing stroke rate and maintain same #of of strokes?

If stroke rate increases and you take the same number of strokes to get across the pool then you are swimming faster.

For instance:

Say it takes 20 strokes to cover the distance of the pool, and you stroke rate is 75 strokes a minute. (60 seconds / 75 stroke) = a stroke every .8 seconds which equals 16 seconds for a length with 20 strokes (20 x .8)

If you swim at 120 strokes a minute you cover that in (60 seconds / 120 stroke) = a stroke every .5 seconds which equal 10 seconds for the length

but if you increased your stroke rate wouldn't it alter the number of strokes per length of the pool?

I was going to make a comment about this in the original post but deleted it to keep it simple. Don't get caught up in stroke count to begin with. If you want to get faster or better swimming there are three things to do:

1) Join a master's group (coach on deck)
2) swim more
3) swim with a partner who is faster than you.

The answer to your actual question is that "it depends". Again the video demonstrates two different stroke rates can be achieved that yield very different types but have the same number of total strokes. I believe the creators are doing this to dramatize it a bit for effect and it is not representative of real-world swimming. In reality you could see a stroke rate increase to cause an increase in strokes, same number of strokes, or decrease of strokes. All three are actual possible which is why I say don't get caught up in strokes to begin with

Thanks