For example, if I have the word "carrot," I can create a new word by appending an "s," to make "carrots." However, it takes longer to say the word "carrots" than it does to say "carrot." Are there any words where you can add a letter (to make a new word), and saying the original word takes more time than saying the new word?
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I'm going by syllables. I think that goes a long way in comparing the duration of typical pronunciations. I'm going for one-letter additions only. (There's quite a few more if you allow two or more extra letters.)
'Boa' has more syllables than 'boat'. Same for 'boa' and 'boar', 'goa' and 'goat' (thanks to user Chris H in the comments), 'goa' and 'goal', 'goa' and 'goad', 'naked' and 'snaked', 'ragged' and 'dragged', 'ague' and 'vague', 'ragged' and 'bragged', 'ave' and 'have', 'ave' and 'cave', 'ave' and 'gave', 'ave' and 'save', 'ave' and 'pave', 'ave' and 'fave', 'ave' and 'eave', 'ave' and 'wave', 'ave' and 'rave', 'ave' and 'nave', 'ave' and 'lave', 'ole' and 'sole', 'ole' and 'role', 'ole' and 'cole', 'ole' and 'mole', 'ole' and 'bole', 'ole' and 'jole', 'ole' and 'hole', 'ole' and 'pole', 'ole' and 'dole', 'ole' and 'vole', 'ole' and 'tole'.
As far as I know, 'boa'/'boat'/'boar' and 'goa'/'goat'/'goal'/'goad' are the only ones where you add the extra letter at the end to come up with a word with fewer syllables.
Somewhat disputable (depending on the preferred pronunciation or meaning of the first word): 'winged' and 'twinged', 'winged' and 'swinged', 'aged' and 'paged', 'aged' and 'raged', 'aged' and 'caged', 'aged' and 'waged', 'aged' and 'gaged'.