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Consider these:
1. The United States at the time when she gained her independence (ca. 1776-1783) was much weaker economically and militarily compared to the British Empire.
2. The United States at the time of the Cold War (ca. 1945-1991) was much stronger economically and militarily than the United Kingdom and her fading Empire.
Those two are facts and have been accepted and widely believed, AFAIK.
However, this begs a question: if the power of United States was continuously increased during 1783-1945 to the point when she outpaced her British counterpart, what was the period when the power of United States and United Kingdom were roughly equal?