Let T be the age of the teacher and S be the age of each student. The average age of the teacher and three students is given by (T + 3S) / 4 = 20. This simplifies to T + 3S = 80. We are also given that the difference between the teacher's age and each student's age is 20 years, which can be represented as T - S = 20. Substituting T = S + 20 into the first equation, we get (S + 20) + 3S = 80, which gives 4S + 20 = 80, so 4S = 60 and S = 15. Therefore, the teacher's age T = S + 20 = 15 + 20 = 35 years.