In survival, I am having issues with my XP grinder. They are a block away from each other and the killing floor is not in the same block as either of them. I do not know how far away I possibly can be for mobs to spawn into the system. I know there is no rep on this question, but I'm kinda raw because I spent the last 6 hours setting this up.
The number of chunks doen't neccessarity have anything to do with whether or not a spawner will be activated. But, rather, how far away a player is from a spawner. By default, a world-generated spawner will activate when a player is within a 16-block radius. Also, spawners can be next to each other and still work, there is no limit on that.
So, in your case, you will have to visit each site in order for the spawners to activate. If you wanted to recreate this in creative mode, you could set a custom spawner with a large "nearby player radius" using commands, but that requires cheats to be enabled in the world.