# A maths question

Discussion in 'Community Discussion' started by Nermal, Jan 26, 2007.

### Staff Member

Joined:
Dec 7, 2002
Location:
New Zealand
#1
Car A is travelling at 25 km/h. Car B is going 3x faster. How fast is Car B travelling?

2. ### mkrishnan Moderator emeritus

Joined:
Jan 9, 2004
Location:
Grand Rapids, MI, USA
#2
Erm... is this a mathematics question or a semantics question? That is, is the active question the difference between "going three times as fast as" and "going three times faster than"?

Typically, at least to an American Engineering-trained mind... the latter phrase should be deprecated.

That is, I typically say:

A is 3x as fast as B -- in this example, 75 km/h

But I don't typically say

A is 3x faster than B
or
A is 300% faster than B

Because it's never clear if the desired answer is 75 km/h or (what I feel is more technically correct) 100 km/h.

3. ### tobefirst macrumors 68040

Joined:
Jan 24, 2005
Location:
St. Louis, MO
4. ### SilentPanda Moderator emeritus

Joined:
Oct 8, 2002
Location:
The Bamboo Forest
#4
3x faster!

At first guess I would actually say 75 km/hr. Although I guess it could be 100 km/hr as brought up above. Most sane people would say 75 km/hr I believe.

5. ### applelabs macrumors member

Joined:
Jan 9, 2007
#5
OK, I'll make a fool of myself...

Assuming you mean can B is moving 3x (three times) faster than car A....
25 km/h x 3 = 75 km/h

So car B is moving at 75 km/h.

6. ### phungy macrumors 68020

Joined:
Dec 5, 2006
Location:
FL/NY/TX
#6
The answer is D, Not enough information given.

That is what I had initially thought but I'm sure the question wasn't worded correctly.

7. ### applelabs macrumors member

Joined:
Jan 9, 2007
#7
Ahh.... Of course. I feel so stupid.

You have to tell us the color/s of each car.

### Staff Member

Joined:
Dec 7, 2002
Location:
New Zealand
#8
Basically I was looking to see whether you guys answered 75 or 100, and I got a mixture of both, which is what I expected.

The reason I bring this up is because Apple uses what I believe to be incorrect notation on their site. For example, the new N AirPort says "5x faster" in some places but "5x the performance" in others; surely 5x faster means 6x the performance.

9. ### mkrishnan Moderator emeritus

Joined:
Jan 9, 2004
Location:
Grand Rapids, MI, USA
#9
See, that's my point, though... traditionally, people *do* say things like "A is 100% faster than B" or "A is 50% faster than B." Both of these statements are clearly meant to be interpreted as implying A is faster than B. They are used commonly and almost invariably in this way.

Specifically, for the car B traveling at 25 km/h

A is 100% faster than B is almost always interpreted to mean that A = 50 km/h
A is 50% faster than B is almost always interpreted to mean A = 37.5 km/h

This latter phrase is never interpreted as A = 12.5 km/h.

So it follows that

A is 300% faster than B should mean A = 100 km/h
and the identical statement:
A is 3x faster than B should mean A = 100 km/h as well.

Which, again, is why I avoid saying this. I think most "trained" or formal users of applied math -- engineers, etc. -- will expect you to mean this when you use this kind of terminology. But I agree that how people who are not professionals will make mixed interpretations.

And now that Nermal tipped his hand, I see that's what he was getting at.

10. ### killmoms macrumors 68040

Joined:
Jun 23, 2003
Location:
Washington, DC
#10
I tend to ignore the words following 5x, as that tells me all I need to know: multiply the old result by 5, get new result. The math of 5x is always the same—I prefer not living in some bizarre world where 5 = 6.

EDIT: Well, no, because they're using percentages faster. When someone says 50% faster, they mean 1.5x as fast (since they're essentially saying it's as fast as the original PLUS half that again). I dislike the old "N% faster" terminology, and prefer straight 1.5x, 2.2x, whatever, since then it's always clear what is meant.

11. ### mkrishnan Moderator emeritus

Joined:
Jan 9, 2004
Location:
Grand Rapids, MI, USA
#11
300% and 3x are the same by definition... at least to me. I feel that most engineers -- the people who actually design the technology that is 5x as fast as whatever -- would agree with that statement. The key word is the one you ignore -- "faster" vs. "as fast." That's exactly why I'm saying I hate using the 3x or 300% faster than.

Joined:
Oct 21, 2003
Location:
Portland, OR
13. ### tobefirst macrumors 68040

Joined:
Jan 24, 2005
Location:
St. Louis, MO
#13
For the record, if I didn't have any reason to believe that there was something more going on than just a simple question (like, if my nephew had asked me while working on homework, for instance) my answer would have been 75.

14. ### nitynate macrumors 6502a

Joined:
Jan 22, 2006
Location:
Clearwater, FL
#14
Wait....

The answer is obvious, it is 100.

Durrr.

15. ### tobefirst macrumors 68040

Joined:
Jan 24, 2005
Location:
St. Louis, MO
#15
The only thing obvious is that the answer is not so obvious. Otherwise half the people wouldn't have said 75.

16. ### killmoms macrumors 68040

Joined:
Jun 23, 2003
Location:
Washington, DC
#16
I think we agree, in a roundabout way.

In fact, lemme boil our argument down into something we can both easily agree on:

Stupid ambiguous English!

17. ### dernhelm macrumors 68000

Joined:
May 20, 2002
Location:
middle earth
#17
Are we all so certain that the question is actually grammatically correct in the first place?

18. ### applelabs macrumors member

Joined:
Jan 9, 2007
#18
No, there is an extra "l" in "traveling".
Besides that, I think it is correct.

From what mkrishnan is saying (I think).
Car B is going 3x faster [than car A].
That means car B's speed equals [(speed of car A + (three times speed of car A)]

19. ### bearbo macrumors 68000

Joined:
Jul 20, 2006
#19
no, (as an engineer too), i think
- 300% faster means (as example of 50% faster, means (0.5+1)x) 300%faster aka (3+1)x = 4x

-however when 3x means 3 times of, which implies whatever it is, is 300% of the previous thing.
edit: however the "3x faster" is controdicting because 3x implies 3 "times of", and followed by "faster" which means 3+1 times of

i do agree with you, tho, that the wording is very ambiguous.

20. ### nitynate macrumors 6502a

Joined:
Jan 22, 2006
Location:
Clearwater, FL
#20
Well, the reason many people said 75 is because they arent making the equation in thier head correctly, or i could be wrong....
I just made 25*3+(12.5*2) in my head and got 100, which is the answer to 3x faster.
[because 12.5 is half of 25 and we are adding the number twice more]

I think.
100 just came to my mind when i did it in my head, i could be wrong.

But i'm not wrong. i am good at math. ahhh! be more specific in your questions.

21. ### bearbo macrumors 68000

Joined:
Jul 20, 2006
#21
enlighten me why you do the 12.5 part?

Joined:
Jul 20, 2006
23. ### phungy macrumors 68020

Joined:
Dec 5, 2006
Location:
FL/NY/TX
#23
That's what I was wondering when I first saw the thread, heh.

24. ### nitynate macrumors 6502a

Joined:
Jan 22, 2006
Location:
Clearwater, FL
#24
Because we are making it 3x as much, which will require half of the original in each number we add to get our final answer.

Isnt that how *x problems work?

25. ### bearbo macrumors 68000

Joined:
Jul 20, 2006
#25
no offend to you, nitynate, but is it just me that has no idea what that means?

when i learend "3x as much" (and that's not even the 3x faster which is very ambiguous).. say a is "3x as much" of b, then a = 3b .. and if b = 25 as in this case, a = 3*25 = 75 (again, i'm talking about 3x as much, not 3x faster in the original post to illustrate how i learnt "3x as much")
but that doesn't involve b/2 anywhere in that equation...