Percentages – What Does ‘X% Faster’ Mean

percentages

I was reading something today that was talking in terms of 10%, 100% and 1000% faster. I assumed that 10% faster means it takes 10% less time (60 seconds down to 54 seconds).

If that is correct wouldn't 100% faster mean 0 time and 1000% mean traveling back in time?

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When I see numbers like that I don't believe they are honest numbers-they really mean "faster", "much faster" and "much much faster". But taking them seriously, if you were traveling 60 mph, 10% faster would be 66 mph (taking 9.09% less time), 100% faster would be 120 mph (taking 50% less time) and 1000% faster would be 660 mph (taking 91.91% less time).

Related Solutions

[Math] “reverse” percentage (go backward instead of forward)

Well...you're mostly in trouble. You cannot possibly calculate the thing you want without (at later points in the loop) knowing when you changed direction.

I'm going to suggest that if you don't need "startTime" in any other place in your code, you treat it as "the time at which I started moving in my current direction"; you'll also need another variable, startPosition, which will be zero in your current code, and direction, which will be $+1$ or $-1$. Then things looks like this:

//initialization
startPosition = 0;
direction = 1;
startTime = 0

// ...other code here


elapsed = (now-startTime)/1000,
t = elapsed/duration; 
percent = (t + startPosition) * 100;
if (percent >= 100){
   percent = 100;
   direction = -1;
   startTime = now;
   startPosition = 100;
}
elseif (percent <= 0){
   percent = 0;
   direction = 1;
   startTime = now;
   startPosition = 0;
}

if( that.reverse ){
   startPosition = percent;
   startTime = now;
   direction = -direction;
}

I've been a little sloppy here, in the sense that when you too a step a little past 100%, I treated it as being 100%, and startedmoving backwards, and similarly at 0%. You COULD do careful truncation and fractional part stuff, but it's almost certainly not necessary, so keep it simple.

[Math] What does $200\%$ faster mean? (How to something be more than $100\%$ faster?)

"Faster" refers to speed (units of something per unit of time) or velocity (units of something per unit of time, with a directional component).

In this case you are talking about charging a battery in $5$ minutes. The speed of that operation is $(1.0\,\text{battery})/(5.0\,\text{minutes})$, or $0.2$ batteries per minute.

$100\%$ faster than $0.2$ batteries per minute would be $0.4$ batteries per minute, or charging a single battery in $2.5$ minutes.

$200\%$ faster than $0.2$ batteries per minute would be $0.6$ batteries per minute, or charging a single battery in $1\frac{2}{3}$ minutes, or $1$ minute and $40$ seconds.

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Related Solutions

[Math] “reverse” percentage (go backward instead of forward)

[Math] What does $200\%$ faster mean? (How to something be more than $100\%$ faster?)

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