Evacuation Centre Capacity and Bus Timing
At 14:00 a bushfire evacuation centre is opening in a school hall. Emergency services expect 320 residents to arrive by 14:30. The main hall has a documented capacity of 180 people. The adjacent sports pavilion has a capacity of 140, but 30% of its floor area is occupied by stored equipment and cannot be used. Buses are available to move overflow to a district stadium 35 minutes away. Each bus carries 45 seated passengers; loading or unloading takes 10 minutes at each end, and buses must return to the centre before making a second trip. The first bus can leave at 14:15. The fire is predicted to affect the school by 16:00. Two buses are available. Residents who cannot board a bus will remain in the hall, but the hall cannot exceed its capacity.
1. Calculate the usable capacity and the overflow if 320 residents arrive by 14:30.
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The main hall provides 180 spaces. The pavilion has a nominal capacity of 140, but 30% is unusable, so the usable fraction is 70%. Usable pavilion capacity = 140 × 0.70 = 98. Total usable capacity = 180 + 98 = 278. If 320 residents arrive, the overflow is 320 - 278 = 42 people. One bus has 45 seats, so a single bus trip can carry all 42 overflow passengers, with 3 seats spare. The plan should still account for late arrivals, because the hall and pavilion would be at capacity once 278 people are inside.
2. With two buses, can the overflow be moved before 16:00? Show the timings. What changes if the expected number rises to 360?
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For 42 overflow passengers, one bus is enough. If loading takes 10 minutes and the first bus can leave at 14:15, loading must start at 14:05. The bus travels 35 minutes, arriving at 14:50; unloading takes 10 minutes, so it is clear at 15:00; the return trip takes 35 minutes, arriving back at 15:35. That is before 16:00. For 360 expected residents, overflow = 360 - 278 = 82. Two buses provide 2 × 45 = 90 seats, which is enough. Each bus takes 41 passengers. Both can load from 14:05, leave at 14:15, arrive at 14:50, unload by 15:00, and return by 15:35, still before 16:00. With only one bus, two trips would be needed; the first returns at 15:35, the second could leave at 15:45 and would arrive at 16:20, which is too late.
3. What is the latest departure time for a bus to complete one round trip by 16:00, and what time should loading start?
Read the worked answer
After departure, a round trip takes 35 minutes outbound + 10 minutes unloading + 35 minutes return = 80 minutes. To be back by 16:00, the latest departure is 16:00 - 80 minutes = 14:40. Loading takes 10 minutes before departure, so loading must start by 14:30. This assumes the bus is available and loading begins promptly. If the bus must also wait for late residents or if unloading is delayed, the departure time must be brought forward. The 14:40 latest departure is a hard limit for a single round trip; it is not the time to begin loading.