I don't know how to do this question

Question

An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 750 meters, and Plane B was at an altitude of 1086 meters. Plane A is losing altitude at 13 meters per second and plane B is losing altitude at 21 meters per second. x is the number of seconds passed. Write an equation to show that the two planes are at the same altitude.

Answer 1

You want two equations for altitude, so that you can solve them for equality.

Both equations are linear equations.

for airplane A:

a(x) = m_Ax + b_A

for airplane B:

b(x) = m_Bx + b_B

we already know most of these numbers. at the time x = 0, we know that A’s altitude was 750, so b_A = 750. Similarly b_B = 1086, so

a(x) = m_Ax + 750

b(x) = m_Bx + 1086

We know how fast they are losing altitude. The are the m values

m_A = -18 ( negative because the altitude is decreasing )

m_B = -21

 

So now we have

a(x) = -18x + 750

b(x) = -21x + 1086

 

since you want to find the value of x ( in seconds) when the altitudes are equal, set a(x) = b(x).

 

-18x + 750 = -21x + 1086

 

You can solve this equation for x to find the time when they were at the same altitude. Substitute it back into the equation to find what the altitude was.