Data Compression. The P2P program compressed the file to a smaller size and recompressed it on your end. It did go faster but it is an illusion.
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He says he was downloading an already compressed file (a zip file which uses the Deflate algorithm by default). Even if the system was uncompressing and recompressing with a better algorithm at each end, such as bzip2 (Burrows–Wheeler algorithm) or xz (LZMA algorithm), he would get at most about a 35% smaller file, which wouldn't account for the double or triple speed he says he got.
I highly doubt a zip file of an mp3 file is even a couple percent compressible.