I'm not sure if player age influences the period, but the doctors do.
with a high level doctor it is likely the player will be back before a full 7 days passed by.
Last time I had a 1 week injury with a level 4 doctor it took 6 days.
But I guess with level 3 doctors or lower it might be 7 days, and more...
They are not your friends; they dispise you. I am the only one you can count on. Trust me.