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After Ray suffers an attack (either stress or heart), Dave says he's not going to the bicycle race with the Italians, even though he's been waiting for this for a long time. Evelyn then shows him her passport, which she uses for ID purposes. It's implied she got it because she was going to travel, but never got a chance to, and this is her way of telling Dave to go after his dreams while he still can. It works.
After Dave loses the race to the Italians because they cheated, he cries on Ray's shoulder. Even Ray is taken aback.