I understand that there is some disagreement over how old Jesus was, and how long His earthly ministry lasted, but as your question states, most scholars believe He started at about 30 years old, and it lasted 3-31/2 years based on tying events mentioned with other established historical dates.
Archaeologists generally date the start of Christ's ministry to the
year A.D. 27. "The beginning of Jesus' public ministry," writes
archaeology professor John McRay, "is dated by synchronisms
[chronological arrangements of events and people] in the Gospel of
Luke (3:1-2). A date of A.D. 27 seems likely . . . The dates mentioned
by Luke are rather well established . . ." ( Archaeology and the New
Testament, 1997, p. 160).
However, I wouldn't be dogmatic on the age or number of years. Scripture isn't explicit, and there is room for error here, leading to several other interpretations, so it might be best to answer "we don't know, but this is why we think..."