Question

Identify the Earth motion that provides the basis for our system of local time and time zones.

Answer 1

The picture is basically not necessary here, what the question is asking is : why do we have different time and different time zones?

Our time is divided into 24 hours, so you could ask: what happens every 24 hours? the answer is: the Earth rotates around its axis. So, the Earth motion responsible for this is its rotation around its axis.

Answer 2

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Time zones are based on longitude. One hour is 15 degrees longitude. west is earlier, east is later.