Academy Block Scheduling With Instructor Ratios and Gear Drying
You are the lead instructor for a Saturday academy session running 0900 to 1130, a 150-minute block. Twelve recruits are available. Two instructors are on duty, including you. Three evolutions are requested: a live-fire drill, 45 minutes, instructor-to-recruit ratio 1:6; a ground ladder drill, 40 minutes, ratio 1:4; and a classroom session on incident command, 30 minutes, ratio 1:12. Each evolution requires a 10-minute changeover for gear and setup, and the changeover counts inside the 150 minutes. Gear from the live-fire drill must dry for at least 30 minutes before it can be used in the ladder drill. Recruits must be supervised at all times and every ratio applies to each group separately. A third instructor is scheduled to arrive at 1000 but has not confirmed. The training captain will not approve any evolution that exceeds the stated ratios.
1. Which of the three evolutions cannot run as written with two instructors, and why? Show the ratio math.
Read the worked answer
The ground ladder drill cannot run with two instructors covering all twelve recruits.
Ratio math:
- Live fire, 1:6, 12 recruits: 12 / 6 = 2 instructors - exactly what you have. Approved.
- Classroom, 1:12, 12 recruits: 12 / 12 = 1 instructor. Approved.
- Ladder, 1:4, 12 recruits: 12 / 4 = 3 instructors. You have 2. Not approved.
Why splitting does not rescue it. Two instructors at 1:4 can supervise 8 recruits on the ladder, but the remaining 4 must be supervised too, and the class ratio is 1:12, which still needs an instructor. That means 3 instructors total: two on the ladder, one with the other 4. With two instructors, the only fully compliant ladder group is 4 recruits (1 instructor, 1:4) while the other instructor supervises 8 recruits in a classroom-type activity.
The trap in this question is thinking a smaller ladder group solves the scheduling problem. It solves the ratio problem but creates a time problem: 4 recruits per 40-minute ladder session means 12 recruits need 120 minutes of ladder time alone, which will not fit alongside the live-fire drill in a 150-minute block.
2. Build the best compliant schedule for the 150 minutes with two instructors, and state what the recruits will not receive.
Read the worked answer
Compliant schedule:
| Time | Activity | Staffing |
|---|---|---|
| 0900-0945 | Live-fire drill, all 12 | 2 instructors (1:6) |
| 0945-0955 | Changeover | - |
| 0955-1025 | Classroom, incident command, all 12 | 1 instructor (1:12); second instructor preps ladder |
| 1025-1035 | Changeover | - |
| 1035-1115 | Ladder drill, 4 recruits, while 8 recruits do classroom review | 1 instructor on ladder (1:4); 1 instructor with the 8 (1:12) |
| 1115-1125 | Changeover and gear return | - |
| 1125-1130 | Debrief | - |
Checks that the schedule passes:
- Live fire ends 0945, so gear is dry at 1015. Ladder starts 1035. The 30-minute drying rule is met with 20 minutes to spare.
- No group exceeds its ratio at any point.
- Total is 150 minutes exactly, with 5 minutes of slack at the end.
What the recruits do not receive: eight of the twelve get no ladder time this session. Only 4 of 12 complete the ladder drill, so the evolution is incomplete as a certification block and must be rescheduled or repeated, not recorded as complete.
3. If the third instructor confirms at 0900, does the full schedule fit? Show the time arithmetic.
Read the worked answer
Yes, it fits, with 5 minutes of slack.
Revised staffing: 3 instructors. Live fire needs 2 (12 / 6), ladder needs 3 (12 / 4), classroom needs 1 (12 / 12).
Schedule:
- 0900-0945 - Live-fire drill, all 12, 2 instructors on the drill and the third on documentation and safety. 45 minutes.
- 0945-0955 - Changeover. 10 minutes.
- 0955-1015 - Classroom, part 1, all 12, 1 instructor. 20 minutes.
- 1015-1025 - Changeover. 10 minutes.
- 1025-1105 - Ladder drill, all 12, 3 instructors. 40 minutes.
- 1105-1115 - Changeover. 10 minutes.
- 1115-1125 - Classroom, part 2, all 12, 1 instructor. 10 minutes.
- 1125-1130 - Debrief. 5 minutes.
Checks:
- Classroom total = 20 + 10 = 30 minutes, the required length.
- Live fire ends 0945; drying completes at 1015; ladder starts 1025, so the drying rule is met with 10 minutes to spare.
- Total 0900 to 1130 = 150 minutes, and the schedule consumes 145, leaving 5.
Key reasoning: the third instructor is what unlocks the ladder drill, not extra time. Without that instructor, no arrangement of the 150 minutes produces a compliant 12-recruit ladder evolution, because the ratio, not the clock, is the binding constraint.