Ele não faz. É uma inconsistência no filme. Teria sido muito confuso para uma audiência que nunca tinha lido os livros para ver um subtítulo "17 anos depois" depois daquela cena, com Frodo ainda com a mesma idade de antes.
Nos livros
Gandalf não viaja diretamente para Minas Tirith depois de visitar Frodo. Ele só o faz 17 anos depois depois do banquete de despedida de Bilbo. Gandalf só viaja para Minas Tirith depois que ele abandona sua perseguição por Gollum.
'With that thought, I forsook the chase, and passed swiftly to Gondor. In former days the members of my order had been well received there, but Saruman most of all. Often he had been for long the guest of the Lords of the City. Less welcome did the Lord Denethor show me then than of old, and grudgingly he permitted me to search among his hoarded scrolls and books.'
Da linha do tempo de Arda:
3001 Bilbo's farewell feast. Gandalf suspects his ring to be the One Ring. The guard on the Shire is doubled. Gandalf seeks for news of Gollum and calls on the help of Aragorn.
3002 Bilbo becomes a guest of Elrond, and settles in Rivendell.
3004 Gandalf visits Frodo in the Shire, and does so at intervals during the next four years.
3008 In the autumn Gandalf pays his last visit to Frodo.
3009 Gandalf and Aragorn renew their hunt for Gollum at intervals during the next eight years, searching in the vales of Anduin, Mirkwood, and Rhovanion to the confines of Mordor. At some time during these years Gollum himself ventured into Mordor, and was captured by Sauron. Elrond sends for Arwen, and she returns to Imladris; the Mountains and all lands eastward are becoming dangerous.
3017 Gollum is released from Mordor. He is taken by Aragorn in the Dead Marshes, and brought to Thranduil in Mirkwood. Gandalf visits Minas Tirith and reads the scroll of Isildur.