South African Mathematics Olympiad

Since $11:45$ is $45$ minutes after $11:00$ and $12:12$ is $60+12=72$ minutes after $11:00$, the length of break is $72-45=27$ minutes.

Alternatively, there are $15$ minutes from $11:45$ to $12:00$ and $12$ minutes from $12:00$ to $12:12$, so the length of break is $15+12=27$ minutes.