This is from Sanjoy Mahajan's The Art of Insight Problem 1.6

Based on the cost of a long-distance plane ticket, estimate the following quantities: (a) the fuel efficiency of a 747, in passenger miles per gallon or passenger kilometers per liter; and (b) the volume of its fuel tank. Check your estimates against the technical data for a 747.

A flight from Melbourne to Las Angeles direct costs about $1,000. There are a number of costs of a long distance flight; such as crew, food, and airport fees. It's reasonable to assume the majority of the cost is fuel. There's also some profit margin for the airline, and allowance for a partially filled plane. Assume fuel is around 80% of the costs, or$800 per passenger.

Jet fuel is more expensive than car fuel (being higher octane), but airlines would get discounts buying the fuel in bulk. Assume that the cost of jet fuel is about the same as petrol $1.50 per litre. Then the fuel usage is$800 per passenger divided by \$1.50 per litre, or 500 litres per passenger.

Melbourne and Las Angeles are roughly on opposite sides of the world. The world is about 6,000 km radius. So halfway around the world is about 15,000 kilometers.

Then the fuel efficiency of a 747 is about 15,000 kilometers divided by 500 litres per passenger, which is about 30 passenger kilometers per litre.

Melbourne to Las Angeles is around the limit of distance for a 747, so it would almost use a full fuel tank. A 747 has about 50 rows of 10 seats, which allows around 500 passengers. So the total volume is about 500 passengers by 500 litres per passenger which is 250,000 litres.

# Checking the results

I can get the specifications of 747s from Wikipedia which references the actual technical sheets.

A 747 can have about 50,000-60,000 US Gallons of fuel which is about 190,000 to 230,000 litres. So my estimate is of 250,000 litres is quite reasonable. This is quite impressive, the plane is about 200 tonnes heavier at takeoff than at landing.

The range of a 747 is about 12,000 kilometers, and typically has about 400 seats. So the fuel efficiency is about 12,000 kilometers x 400 passengers / 250,000 litres, or 20 passenger kilometers per litre. This is not too far from my estimate of 30 passenger kilomters per litre, and is comparable with car travel.