Answer:
[tex]219.2\ sec[/tex]
Step-by-step explanation:
Let
y ----> the altitude in feet
x ----> the time in seconds
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope ot unit rate
b is the y-intercept or initial value
In this problem we have
Your hot air balloon
The slope is equal to [tex]m=4\ \frac{ft}{sec}[/tex]
The y-intercept is [tex]b=0[/tex] ---> represent a proportional relationship
The linear equation is
[tex]y=4x[/tex] ----> equation B
Another aircraft
The slope is equal to [tex]m=-30\ \frac{ft}{sec}[/tex] ---> is negative because is a decreasing function
The y-intercept is [tex]b=7,452\ ft[/tex]
The linear equation is
[tex]y=-30x+7,452[/tex] ----> equation B
Equate equation A and equation B
[tex]4x=-30x+7,452[/tex]
solve for x
Adds 30x both sides
[tex]4x+30x=7,452[/tex]
[tex]34x=7,452[/tex]
Divide by 34 both sides
[tex]x=219.2\ sec[/tex]
