Let x represent the number of seconds that have passed since Firework B was launched.
Let y represent the height the firework after x seconds.From here, we will make a table of values to organize the given information. Note that Firework A is launched 0.25 seconds after Firework B is launched, so to account for the number of seconds it has traveled, we have to subtract 0.25 from x.
Firework A
Firework B
Verbal Expression
Algebraic Expression
Verbal Expression
Algebraic Expression
Number of seconds (s)
x- 0.25
Number of seconds (s)
x
Speed (ft/s)
220
Speed (ft/s)
200
Height (ft)
220( x- 0.25)
Height (ft)
200 x
Set the equation
y= 220( x- 0.25)
Set the equation
y= 200 x
Using this table, we can create the system as follows.
y=220(x-0.25) & (I) y=200x & (II)
The fireworks are set to explode at the same height, so to determine the time at which the firework explodes we must solve for x. To do this, we will use the Substitution Method and substitute the second equation into the first one.
