Time as a percentage

August 13, 2009 2:42 PM

If something takes 2 hours to complete and is then re-run and takes only 1 hour ... is that 100% quicker or 50% quicker?

MathsFilter - maths has never been my strong point! My google-fu has failed me as well.

posted by cantthinkofone to technology (73 answers total)

I would say 50%. Your original time to complete the task was 2 hours. You can now finish it in 1 hour......with a savings of 1 hour. 1 hour / 2 hours = .5
posted by mockjovial at 2:46 PM on August 13, 2009

By my math it is 50% quicker. But if you take 2 hours to do the third run, it will be 100% longer.
posted by weapons-grade pandemonium at 2:47 PM on August 13, 2009

"Quicker" is dependent on how you're defining the word - do you mean the speed of the recording itself, or the amount of time it took to play through the recording? The playback speed increased by 100%, the overall time it took was 50% of the original.
posted by FatherDagon at 2:47 PM on August 13, 2009

It's 50% faster. If something took an hour to run, then took two hours the next time, from that perspective, it's 100% slower.

When you say y is n% <qualifier> than x, the percentage is calculated in terms of x being the whole/100% base.
posted by Brak at 2:47 PM on August 13, 2009 [1 favorite]

It runs twice as fast and takes half as long.
posted by cosmicbandito at 2:47 PM on August 13, 2009 [6 favorites]

It is 100% quicker, and as a consequence the task takes 50% of the time to complete.
posted by thoughtless at 2:47 PM on August 13, 2009 [4 favorites]

The speed is 100% quicker. Say that you're talking about printing a 100 page book. On the first try, you are printing 50 pages/hour, and on the second, you are printing 100 pages/hour, so your rate is twice as fast, or 100% quicker.

On the other hand, you have reduced the time required by 50%. If you did this the other way around (1 hour the first time and 2 the second), you would be increasing the time by 100%.
posted by LittleMissCranky at 2:48 PM on August 13, 2009 [1 favorite]

Now that I think about it again, I have only half of the answer....seconding FatherDagon
posted by mockjovial at 2:49 PM on August 13, 2009

...and thirding. Sorry, I should have read more carefully.
posted by Brak at 2:50 PM on August 13, 2009

50% quicker.

100% = 1
50% = 0.5
2x(0.5)=1x

Going the other direction is a good way to trick people.

200%=2
1(2)=2
2-1=1 therefore an improvement of 100%
But 2 is 200% of 1

Politicians like to confuse people with percentages. There is the total percentage and the amount of change (the difference), which can be expressed as a percentage of the original amount or the new amount.
posted by Xoebe at 2:50 PM on August 13, 2009

On non-preview, the 50% answers are confusing rate and duration. In other words, the rate (quickness) is increased by 100%, but the duration of the task is 50% less.
posted by LittleMissCranky at 2:51 PM on August 13, 2009 [2 favorites]

NO...

100% improvement of anything, no matter what you start with, leaves you with zero.
posted by rahnefan at 2:51 PM on August 13, 2009 [1 favorite]

50% is your answer.
posted by rahnefan at 2:52 PM on August 13, 2009

LittleMissCranky: 100% of 2 hours is 2 hours. Two hours faster than two hours is zero.

If you lose 100% of your money in the stock market you have nothing.
If you lose half of your money in the stock market you must double what you have left to break even.
posted by weapons-grade pandemonium at 2:53 PM on August 13, 2009

It is like when the product offers "50% more" when the original portion was 200g, and it is now 300g.

"Hey, it is only 33% more!"

The answer is: both answers are correct, so chose the one that provides you the best spin on things.
posted by Meatbomb at 2:54 PM on August 13, 2009

If something costs $2 one day, and goes on sale for $1 the next, is it 100% off, or 50% off?

Obviously it's not 100% off, because it would be free then.
posted by blue_beetle at 2:57 PM on August 13, 2009 [1 favorite]

WGP: Two hours is a measure of time, not of speed. You can't, strictly speaking, do something two hours faster. You can only talk about speed in terms of rate, like 50 pages/hour faster in my earlier example. Thus, 100% faster (doubling the speed), or requiring 50% of the time (halving the duration).
posted by LittleMissCranky at 2:57 PM on August 13, 2009

No, Meatbomb. It is 50% more. You then must take off 33% of the new, larger size to get back to the original size. But 33% of the larger size is the same quantity you added to the original size.
posted by weapons-grade pandemonium at 2:57 PM on August 13, 2009

This is a semantic issue. It is not 100% quicker, *you* have completed the task 100% more quickly. Essentially you have competed the task at twice the speed. (So the "100% improvement of anything ... leaves you with zero" argument doesn't hold, you can have 100% increases)

From the other perspective, the task itself has been completed in half the time, so the time taken has been halved. i.e. a 50% reduction in time taken.
posted by biffa at 2:59 PM on August 13, 2009

blue_beetle: but you went in the wrong direction. He was asking about increasing the speed, not decreasing in. If something costs $2 one day $1 the next, it is 50% off. But if something is $1 one day and $2 the next, it has been increased by 100%. Since the OP is talking about speed ("quickness") and not time required, you are increasing, not decreasing. The formula is (difference/original) x 100%, so it does matter in which direction you are moving as well as whether you are discussing speed or duration.

For another example, if you drive 100 miles in 2 hours, then 100 miles in 1 hour, you are going twice as quick (50 mph vs 100 mph), or 100% faster, but you are taking half as much time, or 50% shorter.
posted by LittleMissCranky at 3:02 PM on August 13, 2009

You went from 1/2 an action per hour to 1 action per hour. That is twice as many actions per hour, or 100% quicker.
posted by smackfu at 3:04 PM on August 13, 2009

We're not measuring actions per hour, smackfu. We're measuring time.

LittleMissCranky: "Faster" implies that you are reducing a quantity, namely time. It's like Meatbomb's chocolate bar, or my stock market example. You are reducing the time by half, or 50%, so you are 50% faster. You must then go 100% slower to get back to that 2 hour time.
Don't make me get cranky with you.
posted by weapons-grade pandemonium at 3:05 PM on August 13, 2009

If we're measuring time, then it takes 50% less time. But 50% less time != 50% quicker.
posted by smackfu at 3:07 PM on August 13, 2009

This reminds me of an old Seinfeld joke, which can be summarized thusly: "Q: How far away are you? A: About 10 minutes."

People think of time and distance as the same thing kind of. So when you use a word like "quicker", it's going to be confusing. Some people are going to answer with regards to time, some in distance per time.

For anyone who thinks the answer HAS to be 50% and can't be 100%, let me rephrase the question:

Bob's car can finish a race in two hours (because his car goes 60 mph). Gary's car can finish the same race in one hour (because his car can go 120 mph). Is Gary's car 100% faster than Bob's?
posted by 23skidoo at 3:07 PM on August 13, 2009 [1 favorite]

WPG: you are reducing your quantity of time, but "faster" refers to speed, not to the related quantity of time. If a cop pulls you over and asks you "do you know how fast you were going," do you say, "about 2 hours?"
posted by LittleMissCranky at 3:09 PM on August 13, 2009

Like 23skidoo says, the counterpoint is that other people think: 50% less time == 50% quicker.

No real way to reconcile that.
posted by smackfu at 3:09 PM on August 13, 2009

"Faster" implies that you are reducing a quantity, namely time.

Nope, "sooner" implies that time is being reduced. "Faster" implies that a rate is being increased.
posted by 23skidoo at 3:09 PM on August 13, 2009

This is great! I was really thinking the answer would be obvious and I was just missing it ... I must admit a part of me is happy its not *that* easy a question.
posted by cantthinkofone at 3:09 PM on August 13, 2009 [1 favorite]

If something takes 5 hours to complete and is then re-run and takes only 1 hour, how much quicker is it? 80% or 400%?
posted by smackfu at 3:11 PM on August 13, 2009

Of course, 23skidoo. Gary's car is 100% faster. But he finishes the race 50% quicker, because Bob is only half as quick.
Ever buy and sell currency? I have some Canadian dollars to sell you.
posted by weapons-grade pandemonium at 3:18 PM on August 13, 2009

Piling on -- in this instance, 100%=60minutes. You reduce the time by 30 minutes, you reduce the time by 50%. Double the time (ie add 60min so the total is 120), you increase the time by 100%.

The definition of "quicker" is causing the confusion. Why exactly I can't figure out how to explain, however.
posted by cgg at 3:20 PM on August 13, 2009

Opps -- read the question wrong and used the wrong initial time. The logic still applies however
posted by cgg at 3:21 PM on August 13, 2009

Of course, 23skidoo. Gary's car is 100% faster. But he finishes the race 50% quicker, because Bob is only half as quick.

Go re-read the original question and point out to me where the word "finishes" is. All the question asks is "Is that 100% quicker or 50% quicker?"

It's ambiguous at best.
posted by 23skidoo at 3:24 PM on August 13, 2009

We're not measuring actions per hour, smackfu. We're measuring time.

I think this disagreement is the heart of the issue.
posted by smackfu at 3:27 PM on August 13, 2009 [1 favorite]

The first was 100% slower. The second is 50% faster.
posted by Chocolate Pickle at 3:31 PM on August 13, 2009

Ever buy and sell currency? I have some Canadian dollars to sell you.

Ever write 6th-grade math problems for a living? Questions like these get ripped to shreds by angry parents whose kids are held back because they failed some test at the end of the year. This is not a hard question for me or anyone else to understand. Everyone gets all the math involved. What's hard to understand is exactly WHAT the question wants measured, because it uses poor word choices. It's a question which would be better served by refining the word choices in it so that there is no doubt in anyone's mind what is being asked for. There are TWO things that could be being asked for here, and if you can't see that, it's not me who's the dummy here.
posted by 23skidoo at 3:34 PM on August 13, 2009 [2 favorites]

The confusion is about what exactly "quickness" refers to. Since distance (or work completed) = rate x time, rate and time are inversely proportional for a given task. I argue that "quickness" refers to rate, since "more quick" means more speed, which then leads to less time, rather than the other way around. Other people (maybe with an eye to the title) are using quick to refer to time.

Another way to illustrate: Two runners run for 1 hour. The first runner runs 10 miles, and the second runner runs 5 miles. Given that they ran for the same duration, is one runner quicker than the other?
posted by LittleMissCranky at 3:40 PM on August 13, 2009

I believe the concept we're referring to is % difference.

Essentially (Original # - New #) / Original # = 50%
posted by jourman2 at 3:40 PM on August 13, 2009

I think everyone can agree that it is 50% shorter though.
posted by smackfu at 3:41 PM on August 13, 2009

Go re-read the original question and point out to me where the word "finishes" is.

If something takes 2 hours to complete...

I used "finish" instead of "complete". Do you see a difference between completing a task and finishing a task?
posted by weapons-grade pandemonium at 3:41 PM on August 13, 2009

I don't see how quickness, in standard English, could possibly be interpreted as referring to time rather than to rate, i.e. dimension-divided-by-time. Would someone explain the ambiguity?

Consider whether it makes any sense the other way around, i.e., that "100% slower" would mean something takes twice as long, and "200% slower" would mean it takes three times as long. Because that is the implication of the (incorrect) definition of quicker referring to time rather than rate, assuming you accept slower as the direct opposite of quicker.

In conclusion, quicker = faster = at a higher rate
posted by pengale at 3:43 PM on August 13, 2009

cantthinkofone, congratulations. You have found the next "airplane on a treadmill" question.
posted by smackfu at 3:45 PM on August 13, 2009

OK - it seems the wording of my question may have been poor. I concede that "quicker" is probably a poor choice. Re-reading all the answers it would seem that "faster" would have been a much better choice. I'm going to go with "the re-run being 50% faster than the original". Thanks heaps for all the replies though.
posted by cantthinkofone at 3:46 PM on August 13, 2009

"The re-run takes 50% of the time of the original" is a wording that would be unambiguous.
posted by smackfu at 3:50 PM on August 13, 2009

I used "finish" instead of "complete". Do you see a difference between completing a task and finishing a task?

I will be more direct this time. The question, as stated, does not ask "Is that thing finishing 100% quicker or 50% quicker?" If it said that, then you'd be alot more able to defend your position, assuming you want to argue that colloquially "quicker" means "sooner.

But all it says is "is THAT 100% quicker or 50% quicker?"

What does "that" refer to? It really could refer to the rate at which the items in the question are running. Like Gary's car, which you said was 100% faster than Bob's.
posted by 23skidoo at 3:52 PM on August 13, 2009

Thanks smackfu - I'll go with that
posted by cantthinkofone at 3:53 PM on August 13, 2009

The question only mentions hours. Not miles. Not miles per hour. No distance is mentioned. No rate is mentioned.
posted by weapons-grade pandemonium at 3:59 PM on August 13, 2009

It doesn't have to mention miles, miles per hour, distance or rate. Just because a question only mentions hours doesn't mean that's the only thing you can use to answer the question. Remember this question, that you already replied with "Gary's car is 100% faster"?


Bob's car can finish a race in two hours (because his car goes 60 mph). Gary's car can finish the same race in one hour (because his car can go 120 mph). Is Gary's car 100% faster than Bob's?

Here, now that you already know the answer, I'm making it a liiiiiittle bit harder. Here's the exact same question:

Bob's car can finish a race in two hours. Gary's car can finish the same race in one hour. Is Gary's car 100% faster than Bob's?

The question now only mentions time. Are you going to change your answer? Is Gary's car still 100% faster than Bob's?
posted by 23skidoo at 4:06 PM on August 13, 2009

I'm going to go with "the re-run being 50% faster than the original".

Except that if you mean 'faster' as the speed which the process is done rather than how soon it finishes then you're wrong, it should be 100%. Faster implies rate as it refers to speed, but could be twisted to mean time by referring to how soon something happens (although I think that's a stretch).

So you're still being ambiguous. You need to decide if you want a rate (how fast the task is done) or a length of time (how soon the task is completed) as LittleMissCranky outlined rather nicely above. I agree with 23skidoo that the maths here is pretty straightforward, it's the language that's confusing.
posted by shelleycat at 4:10 PM on August 13, 2009

In computer science there is the concept of 'speedup' that is unambiguous. Although it is usually applied to parallel algorithms, you can use it in any case where you need to compare the time it takes to do something. Basically:

speedup = (time of control task)/(time of new task)

So in this case:

speedup = (2 hours)/(1 hour) = 2

Some people talk about speedup as "'x' times faster", so in this case, the rerun is two times faster than the original run.
posted by demiurge at 4:21 PM on August 13, 2009

It's definitely the rate of the task that I'm interested in.

Let's say I'm wanting to look at a database indexing process (I'm not, but the actualities of my task are far too dull to describe). One day I run the task and it takes 2 hours to complete. System changes are then made and the process re-run, this time it takes 1 hour.

As a percentage I want to express what affect these system changes have had on the rate at which the task was completed.

I'm going to to re-read all of the above and then take a view on what wording would do just that with no ambiguity.
posted by cantthinkofone at 4:23 PM on August 13, 2009

Haven't read any comments. Too lazy. But 'quicker' is referring to the speed. Instead of .5 task-units per hour, you're now doing 1 task-unit per hour. This is a 100% increase in speed, so it's 100% quicker. But it only took 50% as long.
posted by floam at 4:27 PM on August 13, 2009

As a percentage I want to express what affect these system changes have had on the rate at which the task was completed.

If this is what you are getting at, the unambiguously correct answer is that the process ran twice as fast. This is equivalent to saying it ran 100% more quickly. It is also equivalent to saying the process ran in 50% of the time it took before the changes.

Smackfu had the best answer in the thread and I'm not sure what all the confusion is. The original process completed 1/2 cycle per hour. With the changes you now complete 1 cycle per hour.

1/2 cycle per hour to 1 cycle per hour means it is running 100% faster.
posted by Justinian at 4:29 PM on August 13, 2009

100% quicker, it's twice as fast.
posted by Sonic_Molson at 4:43 PM on August 13, 2009

The answer is one hundred per cent. The word that is fooling everyone into believing it's 50% is "quicker".
posted by Zambrano at 5:20 PM on August 13, 2009

I have a question for all you 100 percenters. You have a task that takes two hours. You want to complete it 50% quicker. How long will it take you? Explain your answer.
posted by weapons-grade pandemonium at 5:32 PM on August 13, 2009

100%
consider:
a car travels 2 miles in 2 hours. which is a speed (=quickness) of a mile per hour.
another car travels 2 miles in 1 hour which is a speed of 2 miles per hour.
which is twice as fast as and 100% the quickness of the first car.

You want to complete it 50% quicker. How long will it take you? Explain your answer.
To be clear this is not the same as saying you want to complete it in half the time, but to indulge you:
if it takes me 2 hours to complete a task, I work at a rate of 1/2 a task per hour.
50% faster than that is .75 tasks/hour.
1 task divided by .75 tasks per hour yields 4/3 hours to complete the task at 50% quicker work rate.
posted by juv3nal at 5:43 PM on August 13, 2009

If something takes 2 hours to complete and is then re-run and takes only 1 hour ... is that 100% quicker or 50% quicker?

If it was 100% quicker, the rerun wouldn't take any time at all.

100% of 2 hours is 2 hours, after all.
posted by Blazecock Pileon at 5:44 PM on August 13, 2009

I have a question for all you 100 percenters. You have a task that takes two hours. You want to complete it 50% quicker. How long will it take you? Explain your answer.

Okay, my task is licking 100 envelopes. It takes me 2 hours, so I lick 50 envelopes an hour. If I want to do this 50% quicker, that's 50 + 25 = 75 envelopes an hour. My task is 100 envelopes. If I lick 75 envelopes an hour, it will take me 1 1/3 hours if I want to complete it 50% quicker, like juv3nal said.
posted by 23skidoo at 6:16 PM on August 13, 2009

"...which is twice as fast as and 100% the quickness ofquicker than the first car."

FTFM
posted by juv3nal at 6:36 PM on August 13, 2009

I concede that "quicker" is probably a poor choice. Re-reading all the answers it would seem that "faster" would have been a much better choice.

That change doesn't avoid the problem at all.
posted by ludwig_van at 6:37 PM on August 13, 2009

My question was: "You want to complete it 50% quicker", 23skidoo, because the OP uses the word "complete". You changed that to "do this 50% quicker..." By changing "complete" to "do" you changed a time question to a rate question. I don't mind if the OP wants to change the question to a rate question, but neither distance nor rate is mentioned in the original question. And we are constantly told to just answer the question and not try to guess what question the OP is really asking. But I think there are a few people here who still think that one hour is 100 percent less than two hours, because after all, two hours is 100 percent more than one hour.
posted by weapons-grade pandemonium at 6:45 PM on August 13, 2009

little miss cranky almost nailed it.

in order to put a number to this you need to decide what you are measuring,

total time, or the rate at which the work was done.

If you are measuring the total time the answer is the time is reduced by 50%
As some have correctly pointed out, to reduce the time by 100% would mean the task would happen instantaneously.
In this case you can say "time was reduced by 50%"

If you measure speed then the speed has doubled. In this case the speed has increased by 100%, and you can say "the speed was increased by 100%"

The real problem with this question isn't math, but the ambiguity of language.
I am guessing that if you ask anyone who deals with time and rates as part of their profession they will say unambiguously that saying "something is x% quicker" should mean that the speed has increased by x%.

However, your statement is confusing because you have not said,
"the speed of the re-run is x% quicker" or "the re-run runs x% quicker"
but
"the re-run is x% quicker"

as the explosion of posts on your question shows, many people will interpret this to be referring to the total time of the re run.

I don't think you can can get a way with saying
"the re-run is x% quicker"

i think you need to choose to say either

"the speed of the re-run is x% quicker"
or
"the total time of the re-run was reduced by x%"
posted by compound eye at 6:46 PM on August 13, 2009 [1 favorite]

I read "50% quicker" as 50% shorter time.
If you have a 2 foot board, and you cut it to one foot long, is that 100% shorter or 50% shorter?
posted by weapons-grade pandemonium at 7:06 PM on August 13, 2009

My question was: "You want to complete it 50% quicker", 23skidoo, because the OP uses the word "complete". You changed that to "do this 50% quicker..." By changing "complete" to "do" you changed a time question to a rate question.

I changed nothing about your question. The wording of your question is JUST as ambiguous as the wording of the OP's question. It can be interpreted more than one way.

I don't mind if the OP wants to change the question to a rate question, but neither distance nor rate is mentioned in the original question. And we are constantly told to just answer the question and not try to guess what question the OP is really asking.

Are we really constantly told that? I think that it's pretty clear, even without guessing, that the OP is looking for a way to phrase something so that his meaning is clear. He's not like posing a brainteaser or trying to get AskMe to do his kid's homework. And then he comes in and says exactly that: "Hey, yeah, I wanted to express that the RATE was twice as fast." If that isn't PROOF that the question itself is ambiguous and badly worded, I don't know what is.

But I think there are a few people here who still think that one hour is 100 percent less than two hours, because after all, two hours is 100 percent more than one hour.

Pardon my french, but bullshit. Name people by name who you think believe this. No one in this thread believes that.
posted by 23skidoo at 7:11 PM on August 13, 2009

It's definitely the rate of the task that I'm interested in.

Then it's 100%, as in the rate has increased by 100%, the task runs 100% faster. Although I see Blazecock Pileon is still conflating speed with duration.

I have a question for all you 100 percenters. You have a task that takes two hours. You want to complete it 50% quicker.

You've made the same mistake as the OP and used the same ambiguous term ("quicker"). If you assume 'quicker' refers to rate then 23skidoo has it, if you mean the end of the task comes 50% quicker (i.e. it takes 50% of the time to do) then we're back to one hour. I still think the second version is a weird stretch but it appears that people think that way.
posted by shelleycat at 7:14 PM on August 13, 2009

The discussion above should make it obvious, but if this is for a technical article, either use a well-defined term like speedup or define a new term using a formula that you include in your article.
posted by demiurge at 7:32 PM on August 13, 2009

To take a more extreme example

A task that took 10 hours now takes 1 hour

You are working at a rate of 10 times as fast as you were before
In percentage terms, you are working 1000% the rate you were before.
However, in additive terms (not multiplicative), you are working 900% faster compared to before.

Your task takes 10% as long as it used to.

This is actually very similar to investing or salaries.

You start with a wage of $1 / hr and are promoted to $10/hr.

Your wage increased by $9 or 900%.

You are paid 10x as much as you were before, or 1000% of your old rate.

Similarly, if you bought Google at $1 and the price shot up to $10, your return on investment would be ($10-1)/$1 or 900%. The value of your stock is worth 10 times as much as it was before, or 1000% of what you started with.
posted by chalbe at 8:45 PM on August 13, 2009 [1 favorite]

To answer the OP's question:

You are asking how much you work quicker. Quicker is an adverb to the verb work, in affect asking

Work / Time

So the question is about the rate, and not the duration.

You are then working twice as fast, at 200% the speed of your original task and 100% quicker than your original rate.
posted by chalbe at 8:52 PM on August 13, 2009 [1 favorite]

This is ridiculous: the obvious question is "What is quicker?" Is the amount of time quicker? That makes no sense. Is the speed at which it is being done quicker? Yes! Therefore, the correct answer is that since the speed at which it is being done is increased by 100%, it is 100% quicker.
posted by TypographicalError at 9:48 PM on August 13, 2009

I remember a sports talk radio host once chastised Mario Lemieux as a typical dumb jock because he said he felt "100% better" coming off an injury, which the host felt should equate to Mario feeling the same as he felt earlier. But the key is the addition of the word "better."

If he said he felt 100% of the amount he felt earlier, then yeah, that would apply. But "100% better" means an improvement of 100%, or double. So if he graded himself a 50/100 pre-injury, then he'd now feel 100/100.

If I'm 100 lbs, and Joe Blow is 200 lbs, he weighs 100% more than me. His weight in total pounds is 200% of mine. If he weighed 150 lbs, he'd weigh 50% more than me.

So I'm in the 100% camp. If your production rate was 100 pages an hour, and then it became 200 pages an hour, it'd be 100% more/better/faster. If you went from 100 to 150, it'd be 50% more/better/faster. From 100 to 250 would be 150%. At least, I think.
posted by TheSecretDecoderRing at 3:25 AM on August 14, 2009

(Er, and in case anyone was wondering, the host was talking in reference to comments Mario had made to reporters earlier in the day... lest anyone think #66 was being insulted in person. This was not a Rome/Everett situation.)
posted by TheSecretDecoderRing at 3:36 AM on August 14, 2009

Eureka! Chalbe expressed it most succinctly.

The duration of the job decreased by 50%. "The job went 50% faster (or quicker)."

The rate of work increased by 100%. "The job went 100% faster (or quicker)."

They both mean the same thing. We are both right.
posted by Xoebe at 10:11 AM on August 14, 2009