The continents have gotten so far apart due to movement of tectonic plates.
North America and Africa start drifting from one another about 240 million years ago. These continents moves apart from each other at a rate of one millimeter a year which continues about 40 million years. The movement of tectonic plates is the main cause of this movement which separates two continents from one another and bring ocean between them so we can say that tectonic plates are responsible for the movement of continents.
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