Depends on how you store them. If you put them in the refrigerator, on a shelf and not in a drawer, they'll turn brown pretty slowly.

But don't discount brown bananas. They get mushy but also sweeter. They're not as appetizing if you peel and eat them but they work better for many recipes.

Where I buy bananas the organic ones have a bit of plastic wrap on the top of the stem as here(https://img.thrfun.com/img/230/882/wrap-banana-stems-in-plastic_s5.jpg). You can do it yourself. As bananas ripen they release ethylene which accelerates the browning. This little plastic bit helps contain that so it doesn't spread to the rest of the banana.