Increased nitrogen off-gassing 10ft/3m VS 20ft/6m on 100% oxygen

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Then I think you should screw the physics and look at the physiology instead: the lungs don't fully deflate. Therefore right after gas switch there is a residual air in there that mixes with inspired O2, goes into the tissues, yadda yadda yadda. So there is a non-zero fraction of N2 in there that gets smaller with every breath but is nevertheless there, and is subject to laws of our simple model. QED. (Edit: I mean: you do off-gas faster at 6m, QED.)
This isn't unsolvable. In our limited question, most of the physiological factors are constant so can be ignored. Likewise, I can't see how residual gas would make a difference. You are starting with the same percentages of N2 either way and they are eliminated at the rate (again by percentage). So the PPN2 will match breath for breath.

Do you know the answer to the physics question?

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