This is a decent solution I imagine, I know that in theory 9 rate min could be possible, since the rate is bounded by how fast you can shove the earth and gold trough the conduit and you would only need 2 earths and 1 gold, but i spent waaaay to much on the cost solve to bother to try and optimize this even more. 
But between the cost and rate solve the rate solve is closer to my heart since it just look elegant and effortless, in comparison the cost solve feels ready to go to an asylum.
Really curious what optimizations will come up in the stream for this one.