Let's break down the given situation into a system of linear equations based on the heights of two hot air balloons over time:
1. First Balloon:
- Starts at a height of 3,000 feet
- Decreases in height at a rate of 40 feet per minute
Therefore, if [tex]\( h \)[/tex] represents the height of the first balloon after [tex]\( m \)[/tex] minutes, the equation for the first balloon can be written as:
[tex]\[
h = 3000 - 40m
\][/tex]
2. Second Balloon:
- Starts at a height of 1,200 feet
- Increases in height at a rate of 50 feet per minute
Therefore, if [tex]\( h \)[/tex] represents the height of the second balloon after [tex]\( m \)[/tex] minutes, the equation for the second balloon can be written as:
[tex]\[
h = 1200 + 50m
\][/tex]
Given these two equations, we form a system of equations to represent the situation:
[tex]\[
\begin{array}{l}
h = 3000 - 40m \\
h = 1200 + 50m \\
\end{array}
\][/tex]
Therefore, the correct answer is:
A.
[tex]\[
\begin{array}{l}
h = 3000 - 40 m \\
h = 1200 + 50 m \\
\end{array}
\][/tex]
