Puzzle #66 Carrying Stuff

You have two loads of stuff to carry from point A to point B. You might use one of these three methods:

1. Carry the first load from A to B, go back to A, and carry the second load from A to B.
2. Carry the first load from A one-quarter of the distance to B, go back, and carry the second load to the one-quarter point. Continue advancing in this wise until both loads are at B.
3. #2, but each load leapfrogs the previous one by one-quarter of the distance between A and B.

You would rather travel the least distance. If switching between loads does not add any distance, which of the three methods is best? What other reasons might you have for picking a method?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, September 10, 2014 at noon Pacific Time. I will post the answer shortly after.