Fuel Load for a Coastal Patrol Sortie
A small patrol boat must cover a round trip along a coastline. The outbound leg is 96 km against a current that slows the boat to 12 km/h. The return leg is with the same current, giving a speed of 16 km/h. The boat's tank holds 60 litres, and the engine burns fuel at a constant rate of 4 litres per hour regardless of speed. Before departure the crew chief insists on keeping a reserve equal to one-quarter of the fuel actually used during the trip. The boat must also spend 0.5 hours idling at the turnaround point, burning fuel at the same 4 litres per hour. A crew member claims the boat can complete the trip without refuelling because 'the tank is bigger than the burn.'
1. Determine whether the boat can complete the sortie with the required reserve, showing total fuel used and fuel remaining.
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Outbound time = 96 / 12 = 8 h. Return time = 96 / 16 = 6 h. Idle time = 0.5 h. Total engine time = 8 + 6 + 0.5 = 14.5 h. Fuel used = 14.5 × 4 = 58 L. Required reserve = 58 / 4 = 14.5 L. Total needed = 58 + 14.5 = 72.5 L. Tank holds 60 L, so the boat falls short by 12.5 L. The sortie cannot be flown with reserve intact.
2. The crew proposes shortening the outbound leg so the whole trip (including reserve) fits in 60 L. What is the maximum one-way distance that satisfies the reserve rule?
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Let d be one-way distance in km. Outbound time = d/12, return time = d/16, idle 0.5 h. Fuel used = 4(d/12 + d/16 + 0.5). Reserve = 1/4 of that, so total needed = 1.25 × 4(d/12 + d/16 + 0.5) = 5(d/12 + d/16 + 0.5). Set ≤ 60: 5(d/12 + d/16 + 0.5) ≤ 60 → d/12 + d/16 + 0.5 ≤ 12 → d(4/48 + 3/48) ≤ 11.5 → 7d/48 ≤ 11.5 → d ≤ 78.86 km. Maximum one-way distance ≈ 78.9 km.
3. Comment on the crew member's reasoning that 'the tank is bigger than the burn.'
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The claim confuses raw fuel volume with the required fuel plus reserve. Raw burn is 58 L, which is less than 60 L, so on the surface it looks fine. But the reserve rule adds 14.5 L, pushing the requirement to 72.5 L. The reasoning fails because it omits the reserve constraint and treats 'fits in the tank' as the only test. A correct judgement must compare total requirement (burn + reserve) against capacity, not burn alone.