eat up

1.  Consume completely, as in No television until you eat up your dinner, or This quarter's expenses have eaten up all my spare cash. The literal use (first example) dates from the early 1500s, the figurative from the early 1600s.
2.  Enjoy avidly, as in She simply eats up the publicity. [Late 1800s]
3.  Believe unquestioningly, be gullible, as in He'll eat up whatever the broker tells him. [Slang; early 1900s]
4.  Defeat completely, as in This new fighter just eats up every opponent. [Slang; c. 1830]
5.  See eat out, def. 2.

The verb has 3 meanings:

Meaning #1: finish eating all the food on one's plate or on the table
  Synonyms: finish, polish off

Meaning #2: use up, as of resources or materials
  Synonyms: consume, use up, eat, deplete, exhaust, run through, wipe out

Meaning #3: enclose or envelop completely, as if by swallowing
  Synonyms: immerse, engross, swallow, swallow up, bury