Basic Assumption:
You are running along a latitude line (parallel to equator)

Reason for Assumption:
You cant keep up with the sun nomatter how fast you run if you run perpendicular to the equator (along longitudes)

Anyhow, to be able to keep up with the sun, you must match the angular velocity of earth at that latitude line. As you near the poles (north or south) the normal velocity should decrease therefore we take into account the angular velocity which remains unchanged as it is define in rad/sec or rad/min.

Anyhow, this velocity should change with latitude and the velocity at equator is already derived in the above post.

all the Best~

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