The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young.

How old is Old ?

Let A be the age of Old and B be the age of Young, and d is the difference in their ages at any given time.

At any given time, the age of Young can be expressed as the age of Old minus the difference.

When Old is three times as old as Young (call this time x):
Ax=3Bx=3(Ax-d)
Ax=3Ax-3d
Ax=(3/2)d

When Young will be three times that age (time y):
By=3Ax=(9/2)d

And when Old is half of that age (time z):
Az=(9/4)d
And at that time:
Bz=Az-d=(9/4)d-d=(5/4)d

And now, Old is twice that age:
A=2Bz=(2)(5/4)d=(5/2)d
and of course:
B=A-d=(5/2)d-d=(3/2)d

And we are given that A+B=48.
So:
(5/2)d+(3/2)d=48
4d=48
d=12
A=(5/2)d=30
B=(3/2)d=18

So, Old is now 30.

But, to answer the question posed, "How old is Old?"... I think that whenever you say that with "Old" capitalized, you must mean how old is really really old. So, definitely not 30, or probably even 40. I would venture that someone is Old around 50, 60, or better. Someone is likely OLD when they are upwards of 70 or 80, but that's just my opinion (I'm 20, but still a kid).

Further, I venture that they are both 24. All other times mentioned in the problem are 0.
Old is twice as old (0) as Young was (0) when Old was half as old (0) as Young will be (0) when Young is three times as old (0) as Old was (0) when Old was three times as old (0) as Young (0).

.. I suppose a couple of verb tenses don't quite fit. It seemed clever, anyway.

Posted by DJ on 2003-05-24 20:06:22