Cooldown Reduction Equation

[ysers]

Hi. Not sure where to put this.

Problem:
Ability A has 9 seconds cooldown.
Ability B has 15 seconds cooldown. Everytime you use Ability B. The cooldown of Ability A is reduced by 5 seconds.

Question:
What's the equation to use to figure out the overall cooldown of Ability A (considering Ability B), ie. how many times can you use A in 60 seconds.

Is there any quick equation to figure this out without having to manually count every second ?

 

[JeffM]

Hi. Not sure where to put this.

Problem:
Ability A has 9 seconds cooldown.
Ability B has 15 seconds cooldown. Everytime you use Ability B. The cooldown of Ability A is reduced by 5 seconds.

Question:
What's the equation to use to figure out the overall cooldown of Ability A (considering Ability B), ie. how many times can you use A in 60 seconds.

Is there any quick equation to figure this out without having to manually count every second ?

I am pretty sure that this does belong in odds and ends (at least the way that you have posed it). Please define cooldown.

 

[Romsek]

I am pretty sure that this does belong in odds and ends (at least the way that you have posed it). Please define cooldown.

he's almost certainly talking about a game. You cast a spell, you can't cast it again for some amount of time. That time is the cooldown, or lag is another commonly used term, of the spell. The problem as posted doesn't give enough information to solve it.

 

[daon2]

If I'm reading right, casting B twice reduces the cooldown time for A to -1 seconds, hence infinite castings of A is possible after the 30 second mark

 

[JeffM]

If I'm reading right, casting B twice reduces the cooldown time for A to -1 seconds, hence infinite castings of A is possible after the 30 second mark

Actually after I reached the result that time would reverse direction, I decided that I did not understand the question.

 

[daon2]

Actually after I reached the result that time would reverse direction, I decided that I did not understand the question.

It's simple, it means you could have cast A a second earlier than you did. Casting A 30 times at the 30 second mark means you could have cast it without ever even casting B (but only after using B twice). This may seem paradoxical to those that employ logic, but who needs them

 

[JeffM]

This may seem paradoxical to those that employ logic, but who needs them

Not I. I've been married a long time now.

 

[HallsofIvy]

If I'm reading right, casting B twice reduces the cooldown time for A to -1 seconds, hence infinite castings of A is possible after the 30 second mark

You seem to be assuming that "casting B" results in a permanent reduction in "cooldown time" for A. That is not how I interpret it. I interpret this as meaning that casting B results in a reduction to the next cast of A and only to that one. Also, it is not clear whether you can cast "A" and "B" at the same time. I will assume you can. Also, if you have cast A "n" seconds before B, can you then cast A again 5 seconds from having cast A before or 5 seconds after casting B? I will assume the former.

So you start by casting A and B at the same time. You can then cast A again in 5 seconds. then A again at 14 seconds, then B at 15 seconds, then A at 19 seconds, then A in 28 seconds, then B at 30 seconds, then A at 33 seconds, then A at 42 seconds, then B at 45 seconds, then A at 47 seconds, then A at 56 seconds. You can cast A 9 times in 60 seconds.