Water Rationing on a 120-Hour Navigation Exercise
A 24-person cadet squad (22 cadets, 2 instructors) begins a 120-hour navigation exercise at 06:00 on Day 1. Base camp holds two 300-litre drums: Drum A is three-fifths full and Drum B is one-fifth full. Planned consumption is 3.5 litres per person per day for drinking and 1.2 litres per person per day for cooking and washing. Each cadet also carries a 1.5-litre canteen, refillable only from the drums. A resupply truck is scheduled for 12:00 on Day 3 carrying 400 litres; the drivers warn that about 10 percent is typically lost to spillage and leaking containers. Standing orders require at least 20 litres left in the drums when the squad returns at 06:00 on Day 6. Rain is forecast for Day 5, but the medical officer refuses to count rainwater because collection is not guaranteed. At 06:00 on Day 3 the truck radios a six-hour delay.
1. Using the original 12:00 Day 3 arrival time, calculate whether the squad can finish the exercise while keeping the required 20-litre reserve. Show every total you use.
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Step 1 - Daily demand. Per person: 3.5 + 1.2 = 4.7 L/day. Squad: 24 × 4.7 = 112.8 L/day. Five days: 112.8 × 5 = 564 L.
Step 2 - Supply. Drum A: 3/5 × 300 = 180 L. Drum B: 1/5 × 300 = 60 L. Initial total = 240 L. Usable resupply: 400 × 0.90 = 360 L. Total supply = 240 + 360 = 600 L.
Step 3 - Compare. 600 − 564 = 36 L remaining at the end. The order requires 20 L, so the margin is 36 − 20 = 16 L, roughly 3.4 hours of squad consumption at the planned rate.
Conclusion: yes, the plan works on schedule, but the margin is thin - a single extra use of about 16 L would break the reserve. This is why the delay matters.
2. With the truck now arriving at 18:00 on Day 3, calculate the maximum uniform daily ration per person for the period before resupply if the squad must (a) simply avoid running dry and (b) still hold a 20-litre cushion when the truck arrives. State your assumption.
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Assumption: no other water source is used and the drums are the only supply until the truck arrives.
Draw-down window: 06:00 Day 1 to 18:00 Day 3 = 60 hours. Water available in that window = 240 L.
(a) Arrive with zero. 240 L ÷ 60 h = 4.0 L/h for the whole squad. Per person: 4.0 ÷ 24 = 0.1667 L/h = 4.0 L/person/day.
(b) Arrive with 20 L. (240 − 20) ÷ 60 = 3.667 L/h; ÷ 24 = 0.1528 L/h = 3.67 L/person/day.
So the first 60 hours must be rationed to somewhere between 3.67 and 4.0 L/person/day, against the planned 4.7 - a cut of roughly 15 to 22 percent. A commander would pick near the lower figure, because the 20 L reserve is an order, not a target, and a second delay is possible. Full rations can resume once the truck is unloaded.
3. A cadet argues: 'Even with the delay, just keep drinking 4.7 L per person per day. The truck carries 400 litres, and our canteens hold another 36 litres.' Evaluate this reasoning with numbers.
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When do the drums run dry at 4.7 L/person/day? Squad rate = 112.8 L/day = 4.7 L/h. 240 L ÷ 4.7 L/h = 51.1 hours after 06:00 Day 1, i.e. about 09:00 on Day 3. The delayed truck arrives at 18:00 - roughly 9 hours later.
Size of the gap: 9 h × 4.7 L/h ≈ 42 L short.
Do the canteens save the plan? 24 × 1.5 = 36 L, which is less than the 42 L gap. And the canteens are not extra supply - they are part of the same 240 L, so draining them early simply moves the shortage, leaving the squad at zero with no reserve for a second delay, a casualty, or a hot afternoon.
Verdict: the reasoning is wrong because it compares total supply over five days with demand over five days and ignores timing. Supply and demand must match hour by hour. The fix is to ration to about 3.7–4.0 L/person/day until the truck is unloaded, then restore 4.7 L. Check: 4.0 L/person/day for 60 h uses 240 L; the remaining 60 h at 4.7 L/person/day uses 282 L; 360 − 282 = 78 L left, safely above the 20 L reserve.