What takes the longest to heal torn muscle, torn ligament, or torn tendon? Area is back and knee.

Torn muscle. Healing depends on degree of trauma, type of muscle, location of joints, age, and degree of rest. Like wise so many variable. Some doesn't heal at all without surgical treatment.
Ligament. The real question here is which of these will heal with the most normal return to function. Muscle, because of it's blood supply and structure heals the best of the three. Ligaments have a relatively poor blood supply and when they heal they heal with 'scar' tissue not ligament, which is not as strong. The location of the injury and the injured part's functtion play a key role in this assessment.