Learn Hardcore Korean: jihacheoreun beoseuboda ppareugo beoseuneun jihacheolboda neuryeo. - The subway is faster than the bus, and the bus is slower than the subway.

보다 means “than” in comparisons. The basic pattern is
A는 B보다 + adjective.
So 지하철은 버스보다 빠르다 literally means “The subway is faster than the bus.” In your sentence, 빠르고 is just the connective form of 빠르다 (see next question).

Why is 빠르고 used instead of 빠르다?

-고 is the connective ending that joins two clauses. You take the adjective stem (빠르-) + 고, giving 빠르고, which means “is fast and….” It links the first clause (“The subway is faster than the bus”) to the second (“the bus is slower”).

Why does the second clause use 느려 instead of 느리다 or 느리고?

느려 is the present informal (반말) form of 느리다—you drop -다 and just say 느려.
You don’t need -고 here because it’s the final clause of the sentence, not connecting to anything after it.

What’s the role of the particles 은/는 in 지하철은 and 버스는? Could I use 이/가 instead?

은/는 mark the topic and often set up a contrast. Here you’re contrasting the subway and the bus.

지하철은 = “as for the subway…”
버스는 = “as for the bus…”
You could use 이/가 (subject marker), but 은/는 is more natural when you want to emphasize the comparison between two topics.

Why isn’t there a separate verb for “is” in 빠르고 or 느려?

In Korean, descriptive verbs (adjectives) are self-conjugating verbs. The dictionary form ends in -다 (빠르다, 느리다), and they carry the meaning “to be X” on their own. You don’t need an extra “to be” verb like in English.

Could I say 지하철이 버스보다 빠르고 버스가 지하철보다 느려 instead?

Yes, grammatically it works, but using 이/가 twice makes it sound more like a neutral statement of fact. Using 은/는 adds a contrastive nuance, highlighting “as for the subway vs. as for the bus.” Speakers often choose 은/는 in comparative sentences to emphasize the two topics being compared.