It's a mile, in flowing water with zero visibility, flowing water, and all sorts also in there.
There are only two ways to search such water, one is sonar which as Dis has said has severe limitations, or by getting in the water and trying to feel for it, and the manual process is extremely slow, manpower intensive and likely to miss things because in flowing water you can't be sure you've touched every bit of the bottom, and by the time you say reach a couple of hundred yards down stream (potentially a day or two at least after the missing report*) there is a good chance the body is going to have started to get covered in other debris so you're no longer feeling a nicely outlined body, but potentially something that has a thin layer of sediment and things like dead plant materials.
*Not because you're not trying, but because it takes time to get the necessary teams together to do the search (the police don't have that many underwater search teams), they can only work for so long safely (you don't want to end up with a drowned or hypothermic diver), and it simply takes time to do a methodical search.