Question 79601
See if this helps ..

Let the length of the shorter piece of wood be x centimetres in length.
The longer piece is 20cm longer, so it is (x+20) centimentres long.
.. and the total length of the two pieces put together is 90cm.

so :   x + (x+20) = 90    [as you rightly say]

In this case, we can dispense with the brackets 

      x + x + 20 = 90

Subtract 20 from each side :

     x + x = 70

Which is another way of saying :

    2x = 70

Now halve both sides :

   x = 35 cm  (ANSWER)

If this piece of wood is then cut in half again, then each piece will be 17.5 cm long (ANSWER)  
(if I understand the question correctly)

Hope this helps!