How old is it roughly?
Jelly, 62 bytes

TṀị
“¢&lt;&lt;ð¢‘×\×€0¦7,31,365F⁸:µç“ɲþḣ⁹ḢṡṾDU¤µQƝṁ⁼ẹ»Ḳ¤ṭÇK;⁸Ç&gt;1¤¡”s


A full program printing the result.
(As a monadic link it returns a list of an integer followed by characters)

Try it online!

How?

TṀị - Link 1: list of integers, K; list, V  e.g. [86401,1440,24,1,0,0,0], ["second","minute","hour","day","week","month","year"]
T   - truthy indexes of K                        [1,2,3,4]
 Ṁ  - maximum                                    4
  ị - index into V                               "day"

“¢&lt;&lt;ð¢‘×\×€0¦7,31,365F⁸:µç“...»Ḳ¤ṭÇK;⁸Ç&gt;1¤¡”s - Main link: integer, N  e.g. 3599
“¢&lt;&lt;ð¢‘                                       - list of code-page indices = [1,60,60,24,1]
        \                                     - cumulative reduce with:
       ×                                      -  multiplication = [1,60,3600,86400,86400]
             7,31,365                         - list of integers = [7,31,365]
            ¦                                 - sparse application...
           0                                  - ...to index: 0 (rightmost)
         ×€                                   - ...of: multiplication for €ach = [1,60,3600,86400,[604800,2678400,31536000]]
                     F                        - flatten = [1,60,3600,86400,604800,2678400,31536000]
                      ⁸                       - chain's left argument, N    3599
                       :                      - integer divide         [3599,59,0,0,0,0,0]
                        µ                     - start a new monadic chain, call that X
                                ¤             - nilad followed by links as a nilad:
                          “...»               -   compression of "second minute hour day week month year"
                               Ḳ              -   split at spaces = ["second","minute","hour","day","week","month","year"]
                         ç                    - call the last link (1) as a dyad - i.e. f(X,["second","minute","hour","day","week","month","year"])
                                              -                             "minute"
                                  Ç           - call the last link (1) as a monad - i.e. f(X,X)
                                              -                             59
                                 ṭ            - tack                        [59,['m','i','n','u','t','e']]
                                   K          - join with spaces            [59,' ','m','i','n','u','t','e']
                                           ”s - literal character '
                                          ¡   - repeat...
                                         ¤    - ...number of times: nilad followed by link(s) as a nilad:
                                     ⁸        -   chain's left argument, X  [3599,59,0,0,0,0,0]
                                      Ç       -   call the last link (1) as a monad - i.e. f(X,X)
                                              -                             59
                                       &gt;1     -   greater than 1?           1
                                    ;         - concatenate                 [59,' ','m','i','n','u','t','e','s']
                                              - implicit print - smashes to print  "59 minutes"