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Two hot air balloons are flying above a park. One balloon started at a height of 3,000 feet above the ground and is decreasing in height at a rate of 40 feet per minute. The second balloon is rising at a rate of 50 feet per minute after beginning from a height of 1,200 feet above the ground.

Given that [tex]\( h \)[/tex] is the height of the balloons after [tex]\( m \)[/tex] minutes, determine which system of equations represents this situation.

A.
[tex]\[ h = 3,000 - 40m \][/tex]
[tex]\[ h = 1,200 + 50m \][/tex]

B.
[tex]\[ \begin{array}{l}
h = 3,000 + 40m \\
h = 1,200 - 50m
\end{array} \][/tex]

C.
[tex]\[ m = 3,000 - 40h \][/tex]
[tex]\[ m = 1,200 + 50h \][/tex]

D.
[tex]\[ \begin{array}{l}
h = 3,000m - 40 \\
h = 1,200m + 50
\end{array} \][/tex]



Answer :

GinnyAnswer
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]

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