# Playing audio files at lower % of regular speed - how long will they be? negative percentage / ratio calculation

I got a knot in my brain and can't think of this - I'm sure it's quite simple and I'll be like "duh!" once someone points it out to me...

So the problem is as follows:

An audio file is 30 seconds long. That's 100% of the audio file.

If I play the file at 50% of it's speed it'll be 60 seconds long.

At what percentage do I need to play the song to make it X seconds long? (I am looking for 46.56)

Or in other words if 30 is to 100 the same as 60 is to 50, then what would 46.56 be equivalent to?

To make it $X$ seconds long, play it at $\frac{30}{X}\times 100$ per cent speed.
Since the 50 and 100 refer to "speed" whereas the 30 and 60 refer to "length", it's actually "$100$ is to $1/30$ (i.e., play $1/30$ of the file per second) as $50$ is to $1/60$ (play $1/60$ of the file per second)".
That is, $$\frac{\mbox{speed factor}}{1/\mbox{desired length}} = \frac{{100}}{1/{30}}.$$
Equivalently, $$(\mbox{speed factor}) (\mbox{desired length}) = 100 \cdot 30 = 3000.$$
$$\mbox{speed factor} = \frac{3000}{\mbox{desired length}}.$$