Question about Hubble's constant relating to the age of the universe.

Hi, I've got a question about Hubble's constant that needs clarifying since I know my assumption is wrong, but it feels like the logic used is correct and I am not sure where I am going wrong.

If we consider two sets of galaxies, labeled as Set A and Set B. The galaxies within Set A are receding from us at a velocity of x, while those in Set B are moving away at a higher velocity of y, where y>x. Over time, due to the expansion of the universe, the recession velocity of galaxies in Set A increases until it matches the initial recession velocity of galaxies in Set B, denoted as y.

The question then arises when applying Hubble's Law, which relates the recession velocity of galaxies to their distance from us, thus allowing for the estimation of the universe's age. If we measure the distance and recession velocity of galaxies in Set A at the point their recession velocity equals y, and compare this to the distance and recession velocity of galaxies in Set B when their velocity was initially y, would we obtain the same estimate for the age of the universe? This query hinges on the principle that Hubble's Law provides a linear relationship between the recession velocity of galaxies and their distance from us, which in turn is used to infer the rate of expansion of the universe.

The crux of this inquiry is to understand whether the timing of observing these recession velocities impacts the estimated age of the universe, assuming identical velocities and distances are observed for both sets of galaxies. The linear nature of Hubble's Law suggests that the recession velocity directly correlates with distance, implying that identical velocities would correspond to identical distances, independent of when these observations occur. Consequently, this scenario posits that observing galaxies in Set A reaching a recession velocity of y at a later time should, in theory, yield a similar age estimate for the universe as observing galaxies in Set B with a recession velocity of y at an earlier time.

Thanks for reading.


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