With an electronic system there's not any hours wasted matching, that's the point. You book air, hotel, car. A few days later the air charge comes in, and hooks on to the report. When the trip is over the rental car charge comes in and hooks on. Same for hotel. Employees logs on, adds any charges that weren't pre-booked or paid with AmEx, adds notes to the Amex charges as needed and hits submit.
Compared to the paper reports I filled out at my last job he probably spend a quarter of the time I did. And I bet it's a lot easier for the approver too.