Jim is at home, and it is currently 9:00. He has plans to meet up with a friend later, and has to leave at 9:30 to be on time for it. He decides that, during the half-hour of waiting, he'd get out his computer and work on some stuff he needs to do.
After a while of working, he looks up at the clock, and... oh no! It's 9:45! He's late!
He scrambles out the door and meets up with his friend--late, of course. As he arrives, he wants to explain that he lost track of time, causing him to be late.
And then he remembers he's meeting with the friend that only speaks Japanese.
What expression could he use to convey the same thing as English phrase "lose track of time", or equivalently mean that more time passed than it felt like?