Question

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4057 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 60.75 feet per second and Plane B is gaining altitude at 40.25 feet per second.

How many seconds will pass before the planes are at the same altitude?

What will their altitude be when there’re at the same altitude?

Answer 1

• 46 seconds
• 6851.5 feet

Explanation:

The altitude of each plane can be expressed by an equation that adds the initial altitude and the product of time and its rate of climb.

plane A: y = 4057 +60.75t

plane B: y = 5000 +40.25t

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We want to find the time when their altitudes are the same:

4057 +60.75t = 5000 +40.25t . . . . equate the expressions for y

20.50t = 943 . . . . . . . . . subtract (40.24t +4057)

t = 46 . . . . . . . . . . . . divide by the coefficient of t

At t=46, the altitude of the planes will be ...

y = 5000 +40.25(46) = 5000 +1851.5 = 6851.5

The planes are at the same altitude after 46 seconds.

Both planes will be at an altitude of 6851.5 feet.