How long it takes to boil a brat depends on what you want to achieve. Suppose you only want to infuse the brat with extra flavors and not wholly cook it. In that case, you can simply parboil it before finishing the cooking with another method. In this case, simmering them for under 10 minutes will do the trick.
If you want to slow simmer the brat in beer, allowing them to cook all the way through, you can slow boil them for upwards of 30 minutes to achieve your desired results.