Let Y = the age of the youngest tree
Let M = the age of the middle tree
Let E = the age of the ELDEST tree.  

>>...The age of three grand oaks totals exactly one thousand years...<<

So

Y + M + E = 1000

That's the first equation.

>>...When the youngest tree has reached the age of the middle tree,...<<

The difference between the youngest and middle tree is M - Y

So M-Y is how many years will have passed when the youngest tree has 
reached the present age of the middle tree.

>>... the middle tree will be the age of the oldest tree...<<

So after those M-Y years, the middle tree will be E, the age of the 
Eldest.

So when we add M-Y to the middle tree's age, M, we get E.  Therefore

  M + (M-Y) = E     

That's the second equation.

>>...When the youngest tree has reached the age of the middle tree, 
the middle tree will be...four times the current age of the youngest 
tree...<<

 M + (M-Y) = 4Y

That's the third equation.

So we have this system of three equations in three unknowns

 Y + M + E = 1000
 M + (M-Y) = E
 M + (M-Y) = 4Y
 
which simplies to

 Y +  M + E = 1000
-Y + 2M - E = 0
-5 + 2M     = 0

I assume you can solve that system of equation.

Solution: Y = 133 years
          M = 333 years
          E = 533 years

--------------------------------------------

Checking:

The age of three grand oaks totals exactly one thousand years. 

133 + 333 + 533 = 1000

That checks.

>>...When the youngest tree has reached the age of the middle tree,...<<

That will take 200 years.

>>... the middle tree will be the age of the oldest tree...<<

That checks, because the eldest tree is 200 years older than the 

>>...and four times the current age of the youngest tree...<<

That checks because 4 times 133 is 533.

Edwin