Calculating x% faster than y?

Question

I'm working on an app as a little side project, I can handle the code no problem but I can't get my head around some (fairly basic) math right now.

So, I need a formula, please.

The easiest way I can illustrate my problem is to give an example:

A spell has a cast speed of 0.50 seconds, if I apply an x% cast time buff what is its new speed?

i.e It's base cast time is 0.5s and currently its cast time is +144%

Again, I need a general formula where I can plug in both base times and the % speed increase.

Thanks!

Edit: I made a cardinal error in my first post in not posing the problem properly. Part of my app provides a calculation function for a certain game. The game itself tells you a spells base cast time and in another portion of the game you can see any buffs applied to the spell. The way the game expresses is it is at 200% cast time the spell casts twice as fast. So for a 0.5s spell the cooldown is 0.25 seconds, at 400% it's 0.125s and so on... so a 5000% bonus means you are casting 50x faster. I'm having problems when then numbers are a bit more complicated like 144% etc...

I know this is a strange way of representing things but that's how the game does it and part of my app should show the user what their actual cast time is given the bonuses.

So the spell (in game) is represented as a base time but the buffs are represented as a % increase in speed. - That's what's making my head hurt.

Answer 1

Rate * Time = Distance

1.00 * 0.5 = 0.5

1.44 * T = 0.5

T = 0.5 / 1.44

Answer 2

Percent means literally 'every one-hundred', so if you'd like to say $X$ is $y$ percent of $x$, then you write $$ X = \frac{xy}{100} $$

Examples:

(1) $x = 0.5 \ \text{sec}$ and $y = 144$, then $X=1.44x \ \text{sec} = 0.72 \ \text{sec}.$

(2) $x = 0.5 \ \text{sec}$ and $y = 10$, then $X = 0.1x \ \text{sec} = 0.05 \ \text{sec}.$

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If you would like to be more free with the language and say $X$ is $y$ percent more (or less) than $x$, then you would write $$ X = x + \frac{xy}{100} $$

Examples:

(1) $x = 0.5 \ \text{sec}$ and $y = 44$, then $X = x + 0.44x = 0.72 \ \text{sec}.$

(2) $x = 0.5 \ \text{sec}$ and $y = -90$, then $X = x -0.9x = 0.05 \ \text{sec}.$

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The difference between the two is the language used in expressing $y$, otherwise they are exactly the same.