Race Comment Explainer

Original comment with matches highlighted:

raced keenly in mid-division, pushed along 3f out, rapidly soon after,

Matched phrases & meanings

Phrase	Meaning
Pushed along	The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Mid-division	Running in the middle of the pack.
tailed off	A definitive statement that the horse was finished and effectively out of the race
Weakened	The horse lost speed and dropped back through the field.
Keen	The horse was fighting the jockey, wasting energy early.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Running in the middle of the pack.
A definitive statement that the horse was finished and effectively out of the race
The horse lost speed and dropped back through the field.
The horse was fighting the jockey, wasting energy early.