Depends on the dog, the weather, the terrain, etc. A circle with a one mile radius contains Pi square miles (3.14). That is a significant amount of ground, and dogs aren't a panacea. Usually there are a limited number of canine teams, their training and skill level varies wildly, and you have to focus them on the areas of highest probability.

Little kids can also be problematic, because they've absorbed their "stranger danger" lessons, and some of them also are afraid that they're going to get in trouble for wandering off. So, they sometimes hide and don't make a sound even if ground searchers walk right by. If you're playing hide-and-seek with a tiny tyke in 3+ square miles of rough territory, it's going to take a while.

I vaguely recall a search near here a few years ago where hundreds of searchers did a grid search (i.e. make a tight line and comb the woods) for a kid that had wandered off. The next day the kid popped out from under a dead tree 200 yards from the house. I believe that area had been searched at least twice, and she said she could hear everyone calling her the whole time.