Un segmento de una hora u hora y media.

A period of one hour or one hour and a half.

Caption 40, Rafael T. - La Cultura Maya

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Sooner or later we all notice cases where 'u' replaces 'o' ("or") or where 'e' replaces 'y'  ("and"). These conjunctions change when the word following them starts with the same letter sound. Therefore in the example above, 'o' changes to 'u' because the beginning sound of the next word, hora, is [o] (note that the h is silent).

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The rule of thumb is pretty simple: With the conjunctions o ("or") and y ("and"), the vowels change if they are followed by the same vowel sounds.

Here are some examples of the vowel change in action:

¿Vas a comprar siete cervezas u ocho?
Are you going to buy seven beers or eight?

¿Quieres cervezas o gaseosas?
Do you want beers or sodas?

and...

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Julieta e Ignacio estudian la medicina.
Julieta and Ignacio study medicine.

Yasmil y Javier tocan a la guitarra.
Yasmil and Javier play the guitar.

Try speaking the sentence without changing the vowel and you should hear that it sounds funny to say the same vowel sound twice. That should help you remember this simple rule.