The amount of oxygen required for a trip to the Moon by the fastest mode of transport would depend on several factors, such as the size of the spacecraft, the number of crew members on board, the duration of the trip, and the life support systems used to maintain a breathable atmosphere.

Assuming a spacecraft similar to the Apollo spacecraft used in the 1960s and 1970s, which carried three astronauts and traveled to the Moon in approximately three days, the total amount of oxygen required for the journey would be around 250 kilograms.

This calculation is based on the assumption that each astronaut would require approximately 1 kilogram of oxygen per day to breathe and that the spacecraft's life support systems would need to supply oxygen for both breathing and other purposes, such as powering the spacecraft's engines and systems.

It's worth noting that modern spacecraft designs may have different oxygen requirements depending on their size, duration of the trip, and other factors. Additionally, other gases, such as nitrogen and carbon dioxide, are also required to maintain a breathable atmosphere, so the total amount of gas required for a Moon mission would be greater than just the amount of oxygen.
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