How long will it take a broken elbow to heal?

Depends...: Depending upon the nature of the fracture; conservatively about 2-3 months.

I agree, it depends: This depends on several factors, age (kids heal much more quickly than adults), whether the fracture is widely displaced - suggests greater disruption of blood supply, your underlying medical condition (health people heal more quickly), where the fracture is (which bone, what location) and how the fracture was treated - operatively or non-operatively. Good luck!