Walking at a steady pace you could probably make the trip in less than 20 minutes but trust me you'll stop again and again enjoying the views and the buskers.
The Smithsonian has a nice article by Rick Steves here.
The trail was built as part of the construction of a train tunnel in the 1920s. Before the trail was opened it was a long and difficult journey between Manarola and Riomaggiore. So much that the two villages even had different dialects.
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