Can every flat tire be repaired?
No, and the honest answer matters more than the quick one. A puncture in the central tread area, under about six millimetres wide, can usually be repaired properly with a patch-plug from inside the tire. Damage to the sidewall or the shoulder cannot — there is no safe repair for either, because that part of the tire flexes constantly at speed. A tire that has been driven on while flat is also usually finished, even when the outside looks undamaged, because the internal structure has already broken down. We inspect first and tell you which of those you are dealing with.
