Comment 2 for bug 1090290

Looking a bit closer at that issue, it seems that only the last modification time is taken into account, the access time doesn't seem to matter. The following terminal log should be self-explanatory:

zapman@ubuntu:~/work/bugs/zoo$ touch -d "2004-02-29 16:21:42" testfile
zapman@ubuntu:~/work/bugs/zoo$ zoo -add test1.zoo testfile
Zoo: testfile -- ( 0%) added
zapman@ubuntu:~/work/bugs/zoo$ dir -lha
total 12K
drwxr-xr-x 2 zapman zapman 4.0K 2012-12-14 14:04 .
drwxr-xr-x 4 zapman zapman 4.0K 2012-12-14 13:56 ..
-rw-r--r-- 1 zapman zapman 169 2004-02-29 16:21 test1.zoo
-rw-r--r-- 1 zapman zapman 0 2004-02-29 16:21 testfile
zapman@ubuntu:~/work/bugs/zoo$ touch -d "2005-02-22 16:28:42" testfile
zapman@ubuntu:~/work/bugs/zoo$ zoo -add test2.zoo testfile
Zoo: testfile -- ( 0%) added
zapman@ubuntu:~/work/bugs/zoo$ arj a -hk test2.arj testfile
ARJ32 v 3.10, Copyright (c) 1998-2004, ARJ Software Russia. [18 Dec 2009]

Creating archive : test2.arj
Adding testfile 0.0%
Working...
  1x .
ARJ-PROTECT data size 4096 bytes (3276.8%)
     1 file(s)
AUTO ARJ-PROTECT enabled (1x)
zapman@ubuntu:~/work/bugs/zoo$ dir -lha
total 24K
drwxr-xr-x 2 zapman zapman 4.0K 2012-12-14 14:05 .
drwxr-xr-x 4 zapman zapman 4.0K 2012-12-14 13:56 ..
-rw-r--r-- 1 zapman zapman 169 2004-02-29 16:21 test1.zoo
-rw-r--r-- 1 zapman zapman 4.2K 2012-12-14 14:05 test2.arj
-rw-r--r-- 1 zapman zapman 169 2005-02-22 16:28 test2.zoo
-rw-r--r-- 1 zapman zapman 0 2005-02-22 16:28 testfile
zapman@ubuntu:~/work/bugs/zoo$ date
Fri Dec 14 14:06:21 CET 2012
zapman@ubuntu:~/work/bugs/zoo$ touch -d "2017-02-22 16:28:42" testfile
zapman@ubuntu:~/work/bugs/zoo$ zoo -add test3.zoo testfile
Zoo: testfile -- ( 0%) added
zapman@ubuntu:~/work/bugs/zoo$ dir -lha
total 28K
drwxr-xr-x 2 zapman zapman 4.0K 2012-12-14 14:13 .
drwxr-xr-x 4 zapman zapman 4.0K 2012-12-14 13:56 ..
-rw-r--r-- 1 zapman zapman 169 2004-02-29 16:21 test1.zoo
-rw-r--r-- 1 zapman zapman 4.2K 2012-12-14 14:05 test2.arj
-rw-r--r-- 1 zapman zapman 169 2005-02-22 16:28 test2.zoo
-rw-r--r-- 1 zapman zapman 169 2017-02-22 16:28 test3.zoo
-rw-r--r-- 1 zapman zapman 0 2017-02-22 16:28 testfile