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By the time firework a has been launched, firework b has already been launched for 0.25 seconds, so if we treat the two as equations, then
a = 220 (t)
b = 220 (t) + 220 (.25)
And we want to know when these two equal eachother, as that's they will both detonate.
220t = 200 t + 200 (.25)
20t = 50
t = 2.5