Final answer:
Spain and Portugal established their colonies over approximately 100-125 years, beginning with Columbus's voyage in 1492. Spain was the first to establish a colony in the Americas, and the two Iberian nations faced challenges of distance and governance in their new territories.
Step-by-step explanation:
Establishment of Iberian Colonies
The timespan for Spain and Portugal to establish their earliest colonies in the Americas extends from the late 15th century to the early 17th century. Spain's conquest of the Aztec and Inca empires began with Christopher Columbus's first voyage in 1492 and continued with the fall of the Aztec Empire by Hernán Cortés in 1519-1521, and the Inca Empire by Francisco Pizarro about a decade later. This expansion and colonization phase continued into the 17th century as the Iberian powers worked to set up colonial bureaucracies and institutions of rule. Considering the timeline from the discovery of the Americas by Columbus in 1492 to the extensive colonization efforts throughout the 16th century and beyond, the duration of this process fits a timeline of approximately 100 to 125 years (Option B).
As for which country established the first colonies in the Americas, it was Spain in 1492, followed soon by Portugal. These two Iberian nations led the way in the Age of Discovery and were the first to encounter and subjugate indigenous peoples in the New World. The establishment of these colonies served as models for later European colonization.
Colonial Expansion and Challenges
Spain and Portugal faced significant challenges due to the vast distances between their colonies and Europe. Communication was difficult and slow, and the colonies needed to be economically beneficial to the mother countries. As such, they set up strict systems of governance and trade control, often exploiting indigenous populations for labor.