A bee sat on the head of a horse rider whose horse was trotting eastbound at a steady five miles per hour. Some distance ahead on the same path, another horse and rider were approaching westbound, also at five miles per hour. When the two horses were 20 miles apart, the bee left the first horse rider and flew toward the second horse at a rate of ten miles per hour. Upon reaching the second horse, the bee immediately turned around and flew back at the same rate to the first horse. If the bee kept up this performance until the two riders met, how far (in miles) did he travel from the moment he left the first horse rider?

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