Her sister is 11 years old
Let Hannah age be x
let her sister age be y
since her sister age is 6 years older than one third of hannah age
mathematically,
y = 1/3 * x + 6
Recall that Hannah age is given as 15 from the question
y = 1/3 *15 + 6
1/3 * 15 = 5
y = 5 + 6
y = 11