When NASA was communicating with astronauts on the Moon the time from sending to receiving was 1.28 s What is the distance to the Moon based on this?

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The radio signals travel at the speed of light, approximately 300,000 km/sec (186,000 mi/sec). The distance would be 1.28 x 300,000 or about 384,000 kilometers. *The actual time is an estimate, and the Moon varies in its distance from the Earth from 363,104 km to 405,696 km, so this compares well with the mean distance of 384,400 km.
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