Variable vs hardcoded value in SQL query

Hi Gurus,
I have a SQL query inside a function that looks similar (i'm showing the "where" clause here only) to the below:
WHERE ID = variable_id (by the way this two have exactly the same type, number(20))
and
WHERE ID = 100
In the first option that uses variable it takes 4 secs to complete the query, while the second one that uses hardcoded value completes in milliseonds. Im new to oracle but been to other dbms and havent seen such behaviour. Anyone encountered or know what maybe the cause? I thought of not pasting here the explain plan since its just a question of variable vs hardcoded value.
rgds.

Just want to add something, here is the stats for the two queries:
Statistics for variable_id (15 secs)
29 recursive calls
0 db block gets
24324 consistent gets
21556 physical reads
0 redo size
20676 bytes sent via SQL*Net to client
613 bytes received via SQL*Net from client
25 SQL*Net roundtrips to/from client
17 sorts (memory)
0 sorts (disk)
358 rows processed
Statistics for hardcoded value (5 secs)
4 recursive calls
0 db block gets
2631 consistent gets
0 physical reads
0 redo size
20469 bytes sent via SQL*Net to client
613 bytes received via SQL*Net from client
25 SQL*Net roundtrips to/from client
0 sorts (memory)
0 sorts (disk)
358 rows processed
There are differences consistent gets and physical reads. What coul dbe the problem here?
tnx!

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Database version
Oracle Database 11g Enterprise Edition Release 11.2.0.2.0 - 64bit Production
PL/SQL Release 11.2.0.2.0 - Production
CORE 11.2.0.2.0 Production
TNS for Linux: Version 11.2.0.2.0 - Production
NLSRTL Version 11.2.0.2.0 - Production
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