Convoy Fuel at the 360 Kilometre Mark
A convoy of six vehicles must move 720 km to a forward base. Four vehicles are standard and consume 22 L per 100 km; two carry heavy loads and consume 26 L per 100 km. Every vehicle has a 120 L tank and must arrive at every point with at least 15 per cent of tank capacity remaining. The only refuel point is at the 360 km mark, holding 600 L, of which 150 L is ring-fenced for a separate return party. Consumption figures are for the loaded condition and do not vary with speed over the planned route. No other fuel is available on the route, and vehicles may carry 20 L jerrycans. All vehicles start with full tanks.
1. Can every vehicle reach the 360 km refuel point while keeping the 15 per cent reserve? Show the figures.
Read the worked answer
Reserve: 15% x 120 = 18 L floor. Usable before hitting the floor: 120 - 18 = 102 L.
- Standard: range = 102 / 0.22 = 464 km. Uses 0.22 x 360 = 79.2 L, arriving with 40.8 L (34%).
- Heavy: range = 102 / 0.26 = 392 km. Uses 0.26 x 360 = 93.6 L, arriving with 26.4 L (22%).
Both ranges exceed 360 km, so both classes reach the point legally. The heavy vehicles arrive with less margin (26.4 L against an 18 L floor), which is the class to watch if anything delays the leg.
2. What is the minimum fuel that must be issued at the 360 km point for all six vehicles to finish with the reserve intact, and does the available stock cover it?
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Each vehicle must depart the point holding enough for the remaining 360 km plus the 18 L floor.
- Standard needs 79.2 + 18 = 97.2 L on board; arrives with 40.8 L, so top-up = 56.4 L.
- Heavy needs 93.6 + 18 = 111.6 L on board; arrives with 26.4 L, so top-up = 85.2 L.
Total = 4 x 56.4 + 2 x 85.2 = 225.6 + 170.4 = 396 L.
Available = 600 - 150 = 450 L. Surplus 54 L, so the move is feasible on minimum top-up.
The trap is filling every tank to 120 L: that would take 4 x 79.2 + 2 x 93.6 = 504 L, which exceeds 450 L and would wrongly suggest the plan fails. Minimum top-up, not full tanks, is the correct standard.
3. At short notice the ring-fenced 150 L is released for convoy use, but the return party then requires 150 L to be carried forward from the 360 km point by the convoy itself. Is the serial still feasible?
Read the worked answer
Draw from the point = convoy top-up + fuel carried for the return party = 396 + 150 = 546 L, against 600 L available. Remaining at the point: 54 L, unchanged from the previous task because the release and the new obligation cancel.
Feasible. Check the carriage detail: 150 L at 20 L per can is 8 jerrycans, distributed across six vehicles, so no single vehicle is overloaded, and after top-up no tank is full (97.2 L and 111.6 L), so cans are the only stowage issue.
Assumption to flag: the extra 150 L of jerrycan mass is taken not to alter the stated consumption figures. If it does, the standard and heavy rates rise slightly and the 54 L surplus is the buffer that absorbs it -- so the margin, not the total, is the number to quote.