An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 352 meters, and Plane B was just taking off. Plane A is gaining altitude at 14 meters per second, and Plane B is gaining altitude at 22 meters per second.

Let be the number of seconds that have passed.

(a) For each plane, write an expression for the altitude of the plane after seconds.

Altitude of Plane A (in meters) =

Altitude of Plane B (in meters) =

(b) Write an equation to show that the two planes are at the same altitude.

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.

(To know how much time will it take them to have the same altitude we just have to solve for t:

352 + 14t = 22t

352 = 22t - 14t

352 = 8t

352/8 = t

t = 44 seconds

And the planes will have an altitude of:

Altitude of plane A = 352 + 14*44

Altitude of Plane A = 968 m

Altitude of Plane B = 22*44

Altitude of Plane B = 968 m)