I want to say I was nine when I started mowing grass--with a push mower. But now that I think about it, there is no way I would let my nine year old mow the grass.
Funny how when you're a kid it seems perfectly within your range, but as an adult one can get kind of...into the "lets wrap them in bubble wrap and helmets stage" .
Well...unless it was a non engined mower. Then I'd probably let the kid have a stab at it.