Water Planning for a Three-Day Patrol
Your 27-strong patrol (24 cadets, 3 staff) is on a three-day foot exercise with no water on the route. Planning figures are 4.5 litres per person per day for drinking and 2.0 litres per person per day for cooking and washing. One 4-tonne truck is serviceable and carries a rack of twelve 20-litre jerrycans. A second truck has broken down and will not be repaired before departure. A pre-positioned cache at the mid-point holds 300 litres, all of it usable. Standing orders require you to carry 10 per cent of the total requirement as a contingency, and every litre of that contingency must be physically on the truck or in the cache: there are no streams and no resupply points.
1. Calculate the total water requirement including contingency, and state whether the current plan is workable.
Read the worked answer
Daily requirement per person: 4.5 + 2.0 = 6.5 L Whole patrol, whole exercise: 27 x 6.5 x 3 = 526.5 L With the 10 per cent contingency: 526.5 x 1.1 = 579.15 L
Available:
- Truck: 12 x 20 = 240 L
- Cache: 300 L
- Total: 540 L
540 L against a 579.15 L requirement = a shortfall of 39.15 L. The plan does not work. Note the trap: 526.5 L fits inside 540 L, so a calculation that forgets the contingency produces a comfortable-looking answer that fails on day three. The contingency is not a paper figure here - standing orders say it must be physically present, and 540 L is the physical ceiling.
2. What is the smallest reduction in the daily allocation that makes the plan work, and how many jerrycans does the final figure need?
Read the worked answer
Work backward from the physical ceiling. The 540 L available must cover both consumption and the 10 per cent contingency, so the consumption budget is 540 / 1.1 = 490.9 L. Per person per day: 490.9 / (27 x 3) = 490.9 / 81 = 6.06 L. The current figure is 6.5 L, so a reduction of 0.5 L per person per day is the smallest sensible step that fits.
Check: 27 x 6.0 x 3 = 486 L; plus 10 per cent = 486 x 1.1 = 534.6 L, which is 5.4 L inside the ceiling.
Jerrycans: 534.6 L needs 27 cans at 20 L (540 L). Twelve go on the truck and fifteen come from the cache, which holds 300 L - exactly 15 cans. The cache has nothing to spare, and the margin is under 1 per cent, so one lost or leaking can breaks the plan. Log the cache stock level and inspect cans before loading.
3. The 0.5 L reduction could come from drinking (4.5 to 4.0) or from washing (2.0 to 1.5). Both save exactly 40.5 L. How do you decide, and what would change your answer?
Read the worked answer
The arithmetic cannot decide this - the trade is linear, so both options save identically: 0.5 x 27 x 3 = 40.5 L either way. This is the point at which the numerical answer stops and judgement begins.
Recommendation: cut washing, hold drinking at 4.5 L.
- Drinking water protects cognition, judgement and physical output; the failure mode of under-drinking on a loaded foot patrol in heat is heat illness, which is a casualty, not an inconvenience.
- Hygiene can be substituted: wet wipes, chlorinated hand wash, and a wash at the mid-point cache. The failure mode of under-washing is delayed and manageable.
What would change the answer:
- Forecast above roughly 35 degrees, or heavy loads on long legs - then protect drinking absolutely and find the 40.5 L elsewhere, for example by shortening the exercise by half a day (saves 175.5 L) or cutting staff washing first.
- A route with any usable water source would remove the constraint entirely - check this before rationing anyone.
- Cutting both lines saves 81 L and buys real margin, but only if the medical risk of 4.0 L is assessed and accepted by the commander, not by arithmetic alone.