Answe:
a) Altitude of Plane A (in meters) = 352+24t
Altitude of Plane B (in meters) = 22t
b) 352 + 24t = 22t
Step-by-step explanation:
a) We have that Plane A has an altitude of 352m, and is gaining altitude at 14m/s.
Plane B has an altitude of 0m and is gaining altitude at 22 m/s.
To know the altitudes of Planes A and B we have to add the altitude they have plus the product of the altitude they are gaining and the time in seconds:
An expression for this would be:
Altitude of Plane = x + yt
where:
x is the altitude that they start with, in meters
y is the gaining altitude in m/s
t is the time in seconds
We substitute the values for plane A
Altitude of plane A = 352m + 14m/s *t
We substitute the values for plane B
Altitude of Plane B = 0m + 22m/s*t
Altitude of Plane B = 22m/s*t
b) An equation to show that the two planes are at the same altitude we have to equalize the two expressions of the planes:
Altitude of Plane A = Altitude of Plane B
We can change this to:
352m + 14m/s*t = 22m/s*t
This is the expression.
<em>(To know how much time will it take them to have the same altitude we just have to solve for t:</em>
<em>352 + 14t = 22t</em>
<em>352 = 22t - 14t</em>
<em>352 = 8t</em>
<em>352/8 = t</em>
<em>t = 44 seconds</em>
<em>And the planes will have an altitude of:</em>
<em>Altitude of plane A = 352 + 14*44</em>
<em>Altitude of Plane A = 968 m</em>
<em> </em>
<em>Altitude of Plane B = 22*44</em>
<em>Altitude of Plane B = 968 m)</em>
