When we talk time, I know I can say eleven thirty or half-past eleven for 11:30. But how about eleven and a half? Is it correct?
No. That is not a standard way of talking about time. Have you ever heard anyone use "eleven and a half" when talking about time?
When telling the time, "half past eleven", or "eleven thirty" is correct.
When describing a duration you can say "I was working for eleven and a half hours".