Question

An air trame controller is tracking two planes. To start, Plane A was at an altitude of 820 meters, and Plane 3 was at an altitude of 1234 meters. Plane Alslosing altitude at 15 meters per second, and Plane 8 is losing altitude at 24 meters per secondLet x be the number of seconds that have passed(a) For each plane, write an expression for the altitude of the plane

Answer 1

The equation with both planes at the same altitude is:

`9x=414`

SOLUTION

Problem Statement

We have the equations of descent for two different airplanes, A and B, given in terms of the number seconds (x), as shown below:

`\begin{gathered} Altitude\text{ of plane A, }H_A=820-15x \\ Altitude\text{ of plane B, }H_B=1234-24x \end{gathered}`

We are asked to write the equation to show when the altitudes of the planes will be the same.

Step-by-step explanation

To solve this question, we simply need to equate the two equations given above. This is because the altitudes of the planes are the same.

Thus, we can compute the solution as:

`\begin{gathered} H_A=H_B \\ 820-15x=1234-24x \\ \text{ We need to collect like terms. We do this by adding 24x to both sides,} \\ \text{and subtracting 820 from both sides} \\ \\ 820-820-15x+24x=1234-24x+24x-820 \\ 9x=414 \end{gathered}`

Final Answer

The equation with both planes at the same altitude is:

`9x=414`