Rose-red city half as old as Time
Two professors, one of English and one logic, were having drinks in the local bar. "It is curious," said the professor of literature, "how some poets can write an immortal line and nothing else of lasting value. J. W. Burgon, for example. his poems are so mediocre that no one reads them now, yet he wrote one of the most marvelous lines in English poetry: 'A Rose-red city half as old as Time."
The one devoted to "the science that draws necessary conclusions", improvised a brainteaser, then raised his glass and recited.
"A rose-red city half as old as Time.
One billion years ago the city's age
Was just two-fifths of what
Time's age will be, a billion years from now.
Can you compute
How old the crimson city is today?"
The English professor had long ago forgotten his algebra, so he quickly shifted the conversation to another topic, but you should have no difficulty with the problem, right ?
The one devoted to "the science that draws necessary conclusions", improvised a brainteaser, then raised his glass and recited.
One billion years ago the city's age
Was just two-fifths of what
Time's age will be, a billion years from now.
Can you compute
How old the crimson city is today?"
The English professor had long ago forgotten his algebra, so he quickly shifted the conversation to another topic, but you should have no difficulty with the problem, right ?
Labels: friday special, logic, puzzle
posted by Rajesh Lal at
9:41 AM
43 Comments:
City's age 1BY ago= 2/5(x+ 2BY)
1Bx = 2/5x+800,000,000
1Bx= 0.4x+800,000,000
999999999.6x=800,000,000
x= 0.8 years...
I think thats wrong, afterall... I DID do this at nearing 1 am after a sleepless night...
Oh, wait, It would be
1 billion and 0.8 years old today.
Unless I'm wrong which I probably am.
Erm, hate to be a comment hog, but I would like to point out that its referring to the city of Petra which is somewhere around 9000 years old/
Not sure if this is correct...
Let the city be x today. Therefore time will be 2x.
A billion years ago x = 2/5 (2x + 1B).
Solve for x to get 2B implying that the city was 2 billion years old 1 billion years ago.
So then, it is currently 3 billion years old today.
if the city were 7 billion today, time would be 14. 1 billion years ago the city would have been 6 billion, and 1 billion years from now , time will be 15 billion! 3 goes into 6 twice and 15 5 times giving you 2/5
Time was always flowing, so isn't time's age infinity because it never started nor will it ever stop, it is always there and always going to be moving so therefore it has no age
Let x be city's age today.
So Time's age is 2x.
Then: x - 1 = (2/5)(2x + 1)
Sove, x = 7
The city's age is 7 billion.
Btw Eric, time started at the big bang if you believe that theory.
The Big Bang is the cosmological model of the universe whose primary assertion is that the universe has expanded into its current state from a primordial condition of enormous density and temperature. The term is also used in a narrower sense to describe the fundamental "fireball" that erupted at or close to an initial time-point in the history of our observed spacetime contin.
Theoretical support for the Big Bang comes from mathematical models, called Friedmann models. These models show that a Big Bang is consistent with general relativity and with the cosmological principle, which states that the properties of the universe should be independent of position or orientation.
Also you should read Edgar Allen Poe's work Eureka: A Prose Poem
*****impossible*****
jeditony:
not necessarily because you have to understand that the big bang was responsible for x number of galaxies and if space is ever expanding as the up to date theroy says then there are other galaxies already in existance otherwise the big bang must have been infinite covering the creation of space itself...then you think what was before space?
eric is right time is infinite
it is impossibe to work math with imfinity because, for example infinity/2 =infinity
so again
*****impossible*****
excuse me,
when i said galaxies
i meant to say universies
age of time=2/5*4000000000
aot=1600000000
aot*0.5=800000000
red rose city is 800 million years old.
i spent like half an hour on this and i still think this is completely wrong but it's the best i can do.
I'm sorry buy I just have to come in, I know I've already been commenting but if this man making to puzzle was an actual logisist, he would know that since there is no numerical value for any of the variables, the outcome is also infinite, so there is another reason it is impossible
Its not impossible, just very simple algebra...
If we let x = age of Time now,
and the age of the city now is 1/2 x,
and
1B years ago the city was 2/5 the age of Time 1B years from now, [2/5 = .4]
then
x-1B = .4(x+1B)
x-1B = .4x + 400,000,000
x = .4x + 1,400,000,000
.6x = 1,400,000,000
x = 2,333,333,333 = age of Time
the age of the city = 1/2x =1,166,666,667 years
I can't find a flaw in this, but I only spent a couple minutes on it, and how often do people find flaws in their own thinking when they think they are right?
If you make a simple graph with 5 divisions (for the 5ths) and a "today" mark at the 2nd "fifth" mark, it pretty clearly shows that the age of the city today would be 2.333333333... billion years. I believe the math to back this up is directly above me.
As pointed out already: Seven Billion Years.
Behold my amateur algebra:
R = current age of the Rose-Red City (Milwaukee)
T = current age of Time - an interesting concept in and of itself
B = the number 1,000,000,000, which is kind of a hassle to write all the time.
The Rose-Red City is half as old as Time.
R = 0.5T
One billion years ago, the city's age was two-fifths of what Time's age will be one billion years from now.
R-B = 0.4(T+B)
0.5T-B = 0.4T+0.4B
0.1T = 1.4B
T = 14B
R = 7B
Now check it:
A Billion years ago...
T = 13B
R = 6B
A Billion years from now...
T = 15B
R = 8B
Now will someone please dispute that 6B = 0.4(15B)?
i will
6b=0.4(15b)
/15b /15b
6b/15b=0.4
b(6/15)=0.4
b(0.4)=0.4
/0.4 /0.4
b=1
if that makes sence to anyone.
well its a minute older than it was a minte ago !
(its too late! )
:)
no it means 1 billion years.
well, i've thought it over, and im j=just too lazy to finish thinking it over, so all i'll say is this, If i'd been drinking in the local bar, I could tell you too
I have to go with jeditony on this one. The 2.333 number should have have '1/2*x-1B' on the left side, and it works out to 14B for universe, and 7B for the city
Btw, hivow, your first thing is wrong because if it was 800m years, than 1b years ago it would have been -200m years old -_-
Even in cultures that believe there actually WAS a "beginning of time", that value is either undefined or depicted as analogous to something with an undefined age.
Alright guys, the actual way to do this problem.
"city half as old as time"
2C=T
"one billion years ago the city's age was just two fifths of what times age will be, a billion years from now."
C-1=(2/5)(T+1)
so
C-1=(2/5)(2C+1)
c-1=4C/5+2/5
C/5=7/5
C=7
or the city is 7 billion years old
and
2C=T
14=T
or time is 14 billion years old.
thank you
the city is an infinite # of years old
because:
-time = infinity (yes it does)
-half as old as time = time/2
-because of transitivty also equals:
infinity/2
which is infinity because infinity +,-,/, or x by anything is still infinity
so CITY = INFINITY
^^^^algebreacly jonathan is right
but theretically i'm right
Hate to break it to everyone, but the answer is given in the beginning "A rose-red city half as old as Time." talking about the now, today, the city is half as old as time, one billion years ago, it was one fifth, the only answer it did not provide was one billion years from now.
I've got the city's age as 4.5 billion years.
R = city's age
T = Time's age
A rose-red city half as old as Time:
R = 0.5T
One billion years ago the city's age was just two-fifths of what Time's age will be, a billion years from now:
A billion years ago is T - 1B.
Since R = 0.5T, then a billion years ago R = 0.5 (T - 1B)
But we also know a billion years ago that R = 0.4 (T + 1B)
So,
0.5(T - 1B) = 0.4 (T + 1B)
Solve for T:
0.5T - 0.5B = 0.4T + 0.4B
0.1T - 0.5B = 0.4B
0.1T = 0.9B
T = 9B
Since R = 0.5T = 0.5*9B
R = 4.5 billion years
- Rim
i think that it is just 2/5ths of the earth's age because of 1billon ago + 1 billion ahead is same as where you started.
Simple as this if you have a city half the age of time and one billion years ago it was two-fifths the age of time then in current it would 3/5 and a billion years from now it would be 4/5ths
If the city is x years old today, then time is 2x.
A billion years ago the city would be "x - 1billion"
Which is 2/5 the age of time in 1 billion ie "2/5 (2x + 1billion)
so...
x - 1billion = 2/5 (2x + 1billion)
5x - 5billion = 4x + 2billion
There for the city is 7 billion years old today.
I can safely say the city is older than me
Did anyone take in to account the infinite universe theory?
Maybe that city exists in every state that it ever was in some dimension of time space?
And maybe I can track down Jet Li and take his powers from him?
One can compute rose-red city age to be 7 billion years and the time's age to be 14 billion years, but the question is crimson city age! How could we possibly tell? This is a trick not a puzzle.
i could be wrong here, but i would think that the answer is simple. no matter how long time is, would it not still just be as as old as half of time
course now reading the other comments, i will have to agree with the other erics forst comment about time being infinant
tornado, "crimson" - though having multiple interpretations based on inference - essentially means "red;" Seth, no one can take Jet Li's powers but Jet Li.
arvind, if this is the case then the solution will be:
t = Time’s Age
r = Rose-Red City Age
A rose-red city half as old as Time.
r = 0.5t
One billion years ago the city's age was just two-fifths of what
Time's age will be, a billion years from now.
r-1BN = 0.4(t+1BN)
(0.5t)-1BN = 0.4t+0.4BN
0.5t = 0.4t+0.4BN+1BN
t = 0.8t+2.8BN
0.2t = 2.8BN
t = 14BN
thus,
r = 14BNx0.5
= 7BN
Crimson city is 7 billion years old today.
billion yrs from now = a
billion yrs ago = b
a+b = 2 billion yrs
2-5th off time will be a+b/2-5th
= no good at maths?
ans= 2billion +2-5th of 2 billion
correction
simply saying 2-5th + 3-5th = t
so if 2billion = 3-5th
like i said
no good at maths
age of city = 2/5th + 1 billion
2/5th = 2/3rds of 2 billion
which is 1.333 recurring
so
age of city today =1b + 1.3b = 2.3 billion yrs (too 1 decimal place)
the city is 1.4 billion years old
The age is about 2.3 billion years
x=age
x-1 billion = 2/5 (x + 1 billion)
x - 1 billion = 2/5x + 0.4 billion
3/5x = 1.4 billion
x = 2.3 billion
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