et ha yəladot -> et hayəladot -> et hayladot -> etʰayladot -> etayladot -> tayladot (Copied and added to from Panglossa below)
In fast, casual speech, this reduction tends to happen. It's similar to in English when "it is" becomes "it's", and "they are" becomes "they're". In writing, we can represent casual pronunciation as 'ת, so here it would be הפיל רואה ת'ילדות. However, this is very slangy.
All words in every language are "joined". There's nothing that physically separates words in speech, so only as you become familiar with a language can you start to figure out where the boundaries between words are. If I play you a recording of a language that you've never heard before, you won't be able to say where one word begins and ends, it is just a string of syllables.