How does time dilation effect civilisations?

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Say we had two different civilisations in two different galaxies and an observer in a neutral area of space between the two. We are going to have a race to see which civilisation can develop technology the fastest and reach the observer before the other, both are of the same species and have identical living conditions with identical resources available to them. One galaxy is careering through space vastly faster than the other, but for the sake of argument let's assume both are always equal distance away from the observer. How would velocity and time dilation effect this scenario? The observer in the middle is stationary and it's the two galaxies who are considered dilated, however one galaxy is more dilated than the other. Even though the two civilisations are identical and develop technology at the exact same rate, would one civilisation develop technology and reach the observer faster than the other?
 
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