If the ages of Earth and Moon are nearly identical,...Why are most
rocks found on the Moon so much older than Earth rocks?

Hello.

"If the Moon formed from the Earth, why are the oldest Moon rocks
older than the oldest Earth rocks?

Answer: Although the Earth is older than the Moon, its large size kept
it molten and led to constant resurfacing of the planet due to
volcanic activity and plate tectonics. The Moon solidified relatively
quickly because of its small size, and at least some parts of it have
not experienced much geological activity since then. Thus older rocks
exist on the Moon than on the Earth. "

source:
Astronomy 9, Solution Set, Tony Wong (Instructor)
Australia Telescope National Facility
http://www.atnf.csiro.au/people/twong/ay9/hw/soln5.html

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search strategy:
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I hope this helps.