Fix the service interval
Synthetic service runs 09:00–18:00 on one day. A covers 09:00–13:00 and B 12:00–17:00. Intervals include their start and exclude their end. A minute covered by both counts once; this is presence coverage, not a response or restoration promise.
| Window | Length | Relation |
|---|---|---|
| Service 09–18 | 540 min | Required interval |
| A09–13 | 240 min | Overlaps B12–13 |
| B12–17 | 300 min | Ends before 18 |
Merge before measuring
- Place all endpoints on one timeline
- Merge overlapping coverage
- Subtract the union from service time
An unconfirmed duty window contributes no evidenced coverage.
How many minutes are covered and missing?
Show the worked answer
480 covered and 60 missing. The 60-minute overlap is subtracted:240+300−60=480;17:00–18:00 is uncovered.
Keep the uncovered interval visible
| Case | Decision | Reason |
|---|---|---|
| Add lengths directly | Reject 540 covered | Counts 12–13 twice |
| Merged 09–17 | Accept 480 covered | One continuous eight-hour interval |
The next rota revision must fill 17:00–18:00 explicitly. Moving B earlier increases overlap and does not fill that gap.