Change to interval of an event to gain a certain rate

Yours is an interesting question....and a little hard to think about!!

I'll give it a go and invite others to correct my logic flaws - of which I hope there aren't any.!!!

Let's consider a couple of scenarios;

Suppose I wanted to increase the speed of something twice. Then, this is just a 100% increase. Now, suppose that a process originally took 6 seconds and I wanted it to take just 3 seconds - i.e., twice as fast. Then, I could take 100% and covert it to a decimal, i.e., 1, and then add 1 to this which would give me 2. Now take the reciprocal of this (1/2) and multiply it by the original 6 seconds. So, (1/2)*6 = 3 seconds, and I've doubled the speed.

Well....so far, so good. Now suppose I wanted to triple the speed of some process. Following the above logic, this would be a 200% increase. So, convert 200% to a decimal, i.e., 2, and add 1 to this = 3. Now take the reciprocal of this = (1/3). So, if a process took 6 seconds and I wanted to triple the speed, I'd just multiply the (1/3) times 6 and get 2 seconds - triple the speed of what it originally was.

So....since you want a 55% increase in speed, let's convert this to a decimal (.55) and add 1 to it = 1.55. Now take the reciprocal of this (1/1.55) and multiply it by the time interval of the original process - 2 seconds,. So we have (1/1.55)*(2) = about 1.29 seconds. Thus, a process that originally took 2 seconds now takes 1.29 seconds and we've sped up the process by 55%.

Look this over. I believe it's what you asked for. (Feel free to point out any perceived errors!!)

Guest:

The rate at which an event occurs has an interval of A. Rate is increased by B. What is the reduction to the interval?

Example:

Something occurs every 2 seconds.
I want this rate to increase by 55% (New total would be 155%)
What is the reduction to aforementioned interval to get this new rate?

I agree with CPhill's analysis. Generalising, this is:

Old interval = A
Old rate = 1/A
New rate = (1/A).B = B/A
New interval = A/B
Reduction in interval = A-A/B

With A = 2 and B = 1.55

new interval is

CPhill:

Yours is an interesting question....and a little hard to think about!!

I'll give it a go and invite others to correct my logic flaws - of which I hope there aren't any.!!!

Let's consider a couple of scenarios;

Suppose I wanted to increase the speed of something twice. Then, this is just a 100% increase. Now, suppose that a process originally took 6 seconds and I wanted it to take just 3 seconds - i.e., twice as fast. Then, I could take 100% and covert it to a decimal, i.e., 1, and then add 1 to this which would give me 2. Now take the reciprocal of this (1/2) and multiply it by the original 6 seconds. So, (1/2)*6 = 3 seconds, and I've doubled the speed.

Well....so far, so good. Now suppose I wanted to triple the speed of some process. Following the above logic, this would be a 200% increase. So, convert 200% to a decimal, i.e., 2, and add 1 to this = 3. Now take the reciprocal of this = (1/3). So, if a process took 6 seconds and I wanted to triple the speed, I'd just multiply the (1/3) times 6 and get 2 seconds - triple the speed of what it originally was.

So....since you want a 55% increase in speed, let's convert this to a decimal (.55) and add 1 to it = 1.55. Now take the reciprocal of this (1/1.55) and multiply it by the time interval of the original process - 2 seconds,. So we have (1/1.55)*(2) = about 1.29 seconds. Thus, a process that originally took 2 seconds now takes 1.29 seconds and we've sped up the process by 55%.

Look this over. I believe it's what you asked for. (Feel free to point out any perceived errors!!)

Thanks very much. I was spending ages and somehow could not for the life of me figure out how this would work, even though it is moderately simple. Your method makes complete sense, however I think you could maybe streamline it just a tad by say 55% increase is equal to a total of 155% the speed. and have the "initial interval" multiply by the 1 in the reciprocal making it:

Old interval / (Relative increase + 1)
or
Old interval / total proportional speed

Thanks again

Thanks for your reply.

Yep....I should have "streamlined" it, but.....I was really thinking "out loud" to myself while I was typing!! (LOL!!!)

This problem IS "simple," but it just doesn't seem so at first, does it??

Glad I could help!!!