The Fuel Run
You are driving a supply truck on a training exercise. The fuel gauge shows the tank is 3/8 full. The tank capacity is 120 litres. The route to the depot is 180 km, and the truck consumes fuel at a rate of 1 litre per 4 km. There is a fuel station 60 km ahead, but it is currently closed and will open in 2 hours. You have enough time to wait, but waiting will delay the convoy by 2 hours. Alternatively, you can continue to the depot without refuelling. The convoy must reach the depot within 4 hours. Your current speed is 60 km/h, and you can maintain this speed.
1. Calculate the amount of fuel currently in the tank and determine if you can reach the depot without refuelling.
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Fuel in tank = (3/8) * 120 = 45 litres. Fuel needed for 180 km = 180 / 4 = 45 litres. Since fuel in tank equals fuel needed (45 litres), you can just reach the depot with no fuel to spare. However, this assumes perfect conditions; any delay or detour could cause you to run out. Therefore, it is risky but mathematically possible.
2. Considering the time constraints, should you wait for the fuel station to open or continue? Justify your answer with calculations.
Read the worked answer
Time to reach depot without stopping = 180 km / 60 km/h = 3 hours. This is within the 4-hour limit. If you wait 2 hours at the station, then refuel and continue: remaining distance = 120 km, time = 2 hours. Total time = 2 (wait) + 1 (to station) + 2 = 5 hours, exceeding the 4-hour limit. Therefore, you should not wait; you should continue, but monitor fuel closely.