Convoy Fuel and the 300-Litre Bowser
At 0600 a four-lorry convoy leaves Base A for Forward Operating Base B, 180 km away by the only usable road. Each lorry has a 100-litre tank, starts full, and burns fuel at 1 litre per 4 km on level road. Between kilometre 100 and kilometre 140 the road climbs continuously and consumption on that stretch rises by 25 per cent. Standing orders forbid any vehicle from stopping anywhere with less than 30 per cent of its tank capacity in reserve. The convoy averages 40 km/h on level road and 25 km/h on the climb, and a 15-minute halt is planned at kilometre 100. FOB B holds 300 litres of diesel and no more can be delivered for 48 hours. All four lorries must return to Base A the same day by the same route, and no fuel is available anywhere along the road. Lorry Three has a damaged tank that now holds only 60 litres, though its consumption is unchanged. Radio contact with Base A is reliable throughout.
1. Calculate the fuel a serviceable lorry burns on the outward journey and state whether the reserve rule is satisfied on arrival at FOB B. Show every step.
Read the worked answer
Split the route rather than averaging it, because the climb changes the rate.
Level sections: km 0–100 and km 140–180 = 140 km. At 1 litre per 4 km: 140 ÷ 4 = 35.0 litres.
Climb: km 100–140 = 40 km. Normal burn would be 40 ÷ 4 = 10.0 litres; add 25 per cent: 10.0 × 1.25 = 12.5 litres.
Total outward burn = 35.0 + 12.5 = 47.5 litres.
Reserve check: 30 per cent of a 100-litre tank = 30 litres. Fuel on arrival = 100 − 47.5 = 52.5 litres, which is 22.5 litres above the minimum. The reserve rule is satisfied with a comfortable margin.
Two habits matter here. First, do not apply the 25 per cent penalty to the whole 180 km - it applies only to the 40 km climb. Second, the reserve is a standing order, not a physical limit: a lorry can physically arrive with 12 litres, but doing so is a breach and, in a contested area, an avoidable risk. A useful sanity check is the arrival time: 140 ÷ 40 = 3.5 h, plus 40 ÷ 25 = 1.6 h, plus a 15-minute halt, giving roughly 1125 at FOB B - the fuel plan and the time plan must agree on the same route profile.
2. Can all four lorries complete the round trip using only the 300 litres at FOB B? Quantify the draw on the bowser and state the answer plainly.
Read the worked answer
A lorry must not merely reach Base A; it must reach it with its reserve intact. So work backwards from the reserve, not forwards from empty.
Serviceable lorry (100-litre tank): round trip burn = 47.5 × 2 = 95 litres. Arriving home with the 30-litre minimum means it must leave FOB B carrying 95 + 30 = 125 litres - more than the tank holds. Therefore every lorry must top up at B, but a 100-litre tank caps the top-up: fill to 100 litres. Each arrives at B with 52.5 litres, so each draws 100 − 52.5 = 47.5 litres. That is the cleanest reading: fill every serviceable lorry to the brim at B.
Three serviceable lorries: 3 × 47.5 = 142.5 litres.
Lorry Three (60-litre tank): arrives with 60 − 47.5 = 12.5 litres, draws 60 − 12.5 = 47.5 litres to fill.
Total draw = 142.5 + 47.5 = 190 litres, against 300 available. Yes, the round trip is feasible, with about 110 litres left as contingency - which should be ring-fenced for the return leg or a recovery vehicle, not spent on the outward leg.
Note the honest caveat: on paper every lorry can be filled at B, but Lorry Three arrives at B in breach of reserve (12.5 litres against a required 18). The bowser solves the return problem; it does not solve the outward problem, which is the subject of the next task.
3. Lorry Three's 60-litre tank cannot be enlarged. Plan its fuel so that the reserve rule is respected on both legs, stating the minimum extra fuel and the practical container plan.
Read the worked answer
Outward leg. Reserve for a 60-litre tank = 30 per cent × 60 = 18 litres. Usable fuel within the rule = 60 − 18 = 42 litres. Requirement is 47.5 litres, so the shortfall is 5.5 litres - small, but a breach is a breach.
Practical fix. Carry one 20-litre jerrycan. Burn to the halt point: 100 km level = 25 litres, leaving 35 litres in the tank (above the 18-litre reserve, so legal). At kilometre 100, decant the can: 35 + 20 = 55 litres, which fits because the tank holds 60. The climb then takes 12.5 litres, so Lorry Three arrives at FOB B with 42.5 litres - well inside the reserve.
Return leg. Depart B full at 60 litres. Descend the climb (12.5 litres) to reach kilometre 140 with 47.5 litres. Adding the full 20 litres here would give 67.5 litres, exceeding the 60-litre tank, so decant only 10 litres: tank at 57.5 litres. The remaining 35 km of level road burns 35 litres, so it arrives at Base A with 22.5 litres, above the 18-litre minimum.
Total extra fuel needed: 20 litres outbound plus 10 litres on the return, i.e. 30 litres of jerrycan capacity, with the can refilled at FOB B from the bowser. The general principle: when tank capacity, not fuel availability, is the binding constraint, the answer is distributed refuelling at points chosen so the vehicle is never both low on fuel and inside a reserve-protected state.