Let the age of each student be $x$ years and the age of the teacher be $y$ years. According to the given information, $3x + y = 20 \times 4$, which simplifies to: $3x + y = 80$ …… (1)

Also, $y – x = 20$ …… (2).

By subtracting equation (2) from equation (1), we get: $(3x + y) – (y – x) = 80 – 20$, which simplifies to: $4x = 60$, so $x = 15$ years.

Now, substituting $x = 15$ into equation (2), we get: $y = x + 20 = 15 + 20 = 35$ years.

Therefore, the teacher's age is 35 years.