#### Answer

$2.75$ seconds

#### Work Step by Step

Firework A will fly for x seconds and reach a height of $220x$ feet
Firework B will fly for y seconds and reach a height of $200y$ feet
We are given
$ y=x+0.25\qquad$ ... B flies longer
$ 220x=200y\qquad$ ... they reach the same height
Substitute $x+0.25$ for $y$ in the second equation
$220x=200(x+0.25)$
$ 220x=200x+50\quad$ ... add $-200x$
$20x=50$
$x=\displaystyle \frac{50}{20}=2.5$
Substitute $2.5$ for $x$ in $y=x+0.25$
$y=2.75$
Revert to the meanings of x and y:
Firework A will fly for $2.5$ seconds and reach a height of $220(2.5)=550$ feet
Firework B will fly for $2.75$ seconds and reach a height of $200(2.75)=550$ feet