Planning a School Van Trip with Direct Proportion and Tank Limits
A school van has an 11-litre fuel tank. On a test run it used 4.8 litres to travel 86.4 km at a steady speed. Before an inter-school match the tank contains 6.5 litres. The planned route is: 18 km to pick up players, 214 km to the venue, a detour equal to 12.5% of the venue distance because a bridge is closed, 196 km back by a shorter route, and 22 km of local drops. The driver must keep 1.5 litres in the tank as a reserve because the gauge is unreliable below 2 litres. The school does not want to pay for extra fuel stops unless they are necessary. The driver claims that one refuelling stop will be enough because the tank holds 11 litres.
1. Find the van's mileage in km per litre from the test run.
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Mileage is distance per litre: 86.4 ÷ 4.8 = 18 km/L. This assumes the same steady driving conditions. The later plan should be treated as a direct-proportion estimate, not an exact guarantee, because traffic and load can change mileage.
2. Calculate the total planned distance and the fuel needed, including the 1.5-litre reserve.
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Detour = 12.5% of 214 = 0.125 × 214 = 26.75 km. Total distance = 18 + 214 + 26.75 + 196 + 22 = 476.75 km. Fuel for running = 476.75 ÷ 18 = 26.486... litres. Add reserve: 26.486 + 1.5 = 27.986 litres, about 27.99 litres. The van must consume about 26.49 litres on the road and still have 1.5 litres left.
3. Starting with 6.5 litres, decide whether one refuelling stop is enough. State the minimum additional fuel and a safe refuelling plan.
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Fuel that can be used before touching the reserve = 6.5 − 1.5 = 5.0 litres, giving 5 × 18 = 90 km before the first refuel is needed. Total fuel required = 27.99 litres, so additional fuel needed = 27.99 − 6.5 = 21.49 litres. When the tank is at reserve, a fill to full adds at most 11 − 1.5 = 9.5 litres. One stop can add only 9.5 litres, far short of 21.49 litres. Even two en-route stops at 9.5 litres each add only 19 litres, still short. A safe plan is to fill to full before departure (add 4.5 litres) and then make two en-route refuels, for example 9.5 litres and 7.49 litres. Thus one refuelling stop is not enough.