New Game Mode: Search and Destroy

when I arrive from school I want to do a league of legends game but unfortunately I cant because I only have about 20mins so it would be fun if we added a game mode that can be played in less than 20mins. I was thinking about that and I thought of search and destroy. Basically you are a 5 man team and you only have 1 life if you die its over if you survive about 10 mins its the other teams turn to try and kill everyone on the enemy team.