Quoting sophie:

Hmm I see. Thank you Erdinc.

(If I ever catch my teacher.. )

Quoting erdinc:

"Buçuk" is used after a cardinal number. "Yarım" is used on its own.

iki buçuk saat sonra : two and a half hours later
yarım saat sonra : half hours later

If there is cardinal number (tam sayı preceeding we use buçuk. If there isn't, we use yarım.

Quoting erdinc:

Yes, you got it right.