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I am going to be making all my estimates based on the condition of Bum’s legs in chapters 2, 14 and 17. In chapter 2, we see both of his legs get broken the first day he’s at Sangwoo’s house.
His right leg has sustained a traumatic fracture from hitting the stairs on his way down. I think it’s likely that this is a complete fracture given the amount of swelling, but it’s less severe than the injury to his left leg as it heals faster and/or better. More on his left leg later.
A complete fracture means that there is “discontinuity between two or more bone fragments”(Forensic). Incomplete fractures are more common in children and don’t involve the hard bone actually being split. We can rule these out as 1. Bum is at least in his late 20′s/ early 30′s and 2. the amount of pain and swelling is significantly less than what Bum appears to be going through.
We can see that while it’s still sore here, he can support a fair amount of weight on his right leg. It’s pretty impossible to say the exact type of fracture without an X-ray, but given that the injury was caused by a short, hard impact from one direction, I would say it's a transverse fracture. This means that the bone is split perpendicular to the point of impact and seems the most likely if we assume that injury was caused by a single impact with one of the stairs.
Now, this type of bone injury takes about 6-12 weeks to heal enough to walk on with proper treatment. At this stage a hard callus has formed around the break, but new bone has not had time to fully form.
This gives us a minimum time frame of 6 weeks, but seeing as Bum never got proper treatment, and likely had further injury to the area given Sangwoo’s abuse, I think it’s likely that it would take closer to the 12 weeks for his leg to heal enough to support weight. He is also malnourished as we can see by his weight loss.
I’ve seen a couple other posts talking about this, and just look. On the right left is bum in chapter 2 (the day he arrives) and on the right chapter 14. He was skinny before, but the bones in his wrists and arms did not protrude the way they do now. This difference could be stylistic, but from what we know of Sangwoo’s treatment, I think it is safe to assume that Bum has not been eating well.
This is important because bone heals much slower without proper nutrients and calcium. The exact amount this would extend his healing period is hard to determine, but it strengthens my belief that it would have taken closer to 12 weeks for Bum’s right leg to heal enough to support weight.
Altogether this puts my minimum estimate, for Bum to be able to walk at all, at 8-12 weeks.
Now, Bum’s left leg is a different story. While once again, it is impossible to tell the exact extent of his injury past a complete fracture, we can assume that it is worse than his right. For starters, the way his left is broken is much more traumatic.
Just looking at the size of the hammer and how hard Sangwoo hits Bum, we can assume that this fracture is pretty severe. Even though this is again a single impact, given the size of the hammer’s head it is more likely than not that this is a comminuted fracture.
A comminuted fracture is the technical term for shattered bone; two or more fragments are completely detached from the rest. This could also be a compound fracture, meaning pieces of bone have broken through the skin. While we never see the true extent of Bum’s injuries, he doesn’t appear to be bleeding or have any serious deformity in chapter three so we can rule this out.
With a fracture this severe, casting and sometimes surgery are necessary to prevent malformity. This means, best case scenario, Bum is lucky enough to not have any pieces seriously out of place and will heal with a lumpy, but somewhat usable leg.
Bum’s left leg takes longer to heal as we can see in chapter 17; this fits my theory that he suffered a comminuted, or at least more severe, transverse fracture. He is able to support a fair amount of weight on his right, but must still use a crutch on his left to walk.
Most bone forms a hardened fracture callus in 6-8 weeks with full bone growth finishing around 12 weeks. However, as I’ve already established, Bum has not received proper treatment or nutrients to expedite the healing process. My estimate remains around 8 weeks for weight bearing and 12-14 for full healing.
Here is where we come into a bit of a problem getting an exact time frame. If Bum’s left leg injury is transverse rather than comminuted, it is more likely he has been healing for 7-10 weeks and his right is in better shape simply because it was less fractured and was able to heal faster.
However, if his left leg really did sustain a comminuted fracture, it is possible both legs have had time to heal fully and his need for crutches is due to malformity rather than incomplete healing. This would put his time frame at 12+ weeks as even after his left leg had finished healing, it still wouldn’t be able to support weight well.
I doubt that Bum has been been a prisoner much longer than 3 or 4 months because we see that his right leg has not finished healing in chapter 14 as he has pain and difficulty walking through the store.
It’s unclear how much time has passed between the 14 and 17, but I doubt that it was longer than a couple weeks. This is given that Koogi seems not to skip ahead much longer than that.
Also, my estimate of 8-12 weeks for Bum to be able to walk nicely fits chapter 14. The healing between 14 and 17 could have taken anywhere from 1-3 weeks seeing as he goes from being able to painfully support weight, to only needing a crutch for his left leg.
Conclusion: Bum has been a captive somewhere between 8 and 12 weeks as of chapter 14, and between 9 and 15 weeks as of chapter 17.