[Rails] "belongs_to" two different people

I have a People table and a Tasks table. Some People are Managers, some
are Workers. Each Task has a Manager and a Worker.

How do I define the relationships? I tried a STI setup, where Managers
and Workers inherit from People, and People has a type column. In my
Task table, I have worker_id and manager_id rows. Then:

task belongs_to worker
task belongs_to manager
worker has_many tasks
manager has_many tasks

But when I ask for task.worker, or task.manager, it throws an error.

How can I do this without separate Worker and Manager tables?
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