Solving a word problem using a system of linear equations of the form y=mx+b

Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2652 feet and Plane B is just taking off. Plane A is gaining altitude at 30.5 feet per second and Plane B is gaining altitude at 85.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitude be when they're at the same altitude?

Answer 1

Let x be time in seconds and y1 and y2 be the height of the planes at x seconds.

The equation for Plane A is given by,

y1 = 30.5x + 2652 -----------------(1)

The equation for Plane B is

y2 = 85.75x  -----------(2)

The planes meet when y1=y2, so

85.75x = 30.5x +2652

or 85.75x - 30.5x = 2652

or 55.25x = 2652

or x = 2652/55.25

or x = 48

Now, putting the value of x in eq(2) we get:

y2 = 85.75(48) = 4116 feet

After 48 seconds both plane will be at 4116 feet of height