A Boeing 767 due to fly from Montreal to Edmonton required refueling. Because the fuel gauge on the aircraft was not working, a mechanic used a dipstick to determine that 7682 L of fuel were left on the plane. The plane required \(22,300 \mathrm{kg}\) of fuel to make the trip. In order to determine the volume of fuel required, the pilot asked for the conversion factor needed to convert a volume of fuel to a mass of fuel. The mechanic gave the factor as \(1.77 .\) Assuming that this factor was in metric units (kg/L), the pilot calculated the volume to be added as 4916 L. This volume of fuel was added and the 767 subsequently ran out the fuel, but landed safely by gliding into Gimli Airport near Winnipeg. The error arose because the factor 1.77 was in units of pounds per liter. What volume of fuel should have been added?

Step by step solution

01

Calculation of Fuel Volume in Proper Units

The first step is to convert the weight of the required fuel from kilograms to pounds, since the provided conversion factor is in pounds per liter. Here's how this can be done:We know that 1 kg is approximately 2.20462 pounds. So we multiply 22,300 kg, the total weight required for the trip, by this factor to convert it to pounds.\[22,300 \mathrm{kg} \times 2.20462 \mathrm{lb/kg} = 49,172.966 \mathrm{lb}\]

02

Calculation of Required Fuel Volume

Now that we have the weight in pounds, we can divide it by the correct conversion factor (1.77 lb/L) to find the required fuel volume:\[49,172.966 \mathrm{lb} \div 1.77 \mathrm{lb/L} = 27,781.87 \mathrm{L}\]

03

Calculation of Additional Required Fuel After Considering Initial Fuel Volume

The calculation above gives us the total volume of the fuel required for the trip. However, we must subtract from this the volume of the fuel that was already in the plane (7682 L) to find out how much extra fuel was needed:\[27,781.87 \mathrm{L} - 7682 \mathrm{L} = 20,099.87 \mathrm{L}\]

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