How to sync a 20 seconds sprint game

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Hey guys,
I'm making a mobile multiplayer.
I simulate a lobby (inside a room) when all players have the "ready" key in their properties, The MasterClient can click Start Game.
Now when the game is started, all players are declared, there is a 3,2,1 GO, and then, a 20 seconds session of bananas collecting should start.
At the end of those 20 seconds all players are unable to collect more bananas and all players should check all the scores and calculate the ranks (1st place, 2nd place, etc...).

Now the question is:
How can I really make sure that the game is running 20 seconds?
If the admin is the one who counts the time and he minimizes the app after 19 seconds, all the other players are waiting for the admin end of 20 seconds q, that will never come (because his app is minimized).

How can I achieve a real "end of 20 seconds" que ?
Can I (as a Master Client) tell the server to change the room properties after X amount of time? and the server would do it even if I (as a Master Client) disconnect from the room?

Please help me with this issue? I'm in a big dilema about how to implement a real state sync with the option of players minimizing their apps..

Thanks! :)