Short answer: it has to be back-to-back.
Longer answer: The Earth-to-Moon series are just special forms of standard Saddlesore and Bun Burner rides with the standard time limits. As the rules state,
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Several combinations of the standard IBA Bun Burner, Bun Burner Gold and SaddleSore rides are acceptible for certification. The following IBA standard rides can be applied to the Earth to Moon Adventure series of rides:
SaddleSore 3,000 in less than 72 hours
SaddleSore 3,000 Gold in less than 54 hours
Bun Burner 1,500 in less than 36 hours
Bun Burner Silver in less than 30 hours
Bun Burner Gold in less than 24 hours
Bun Burner 3,000--2 BBGs back to back
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So you are fine to do a Bun Burner, spend time with friends, and do another Bun Burner back. But unless you were doing one of the 3,000-mile rides (in which case your time with friends would be very, very short
) they would be considered two separate one-way rides as opposed to a single round trip.
Ira Agins
Iron Butt Association