Select the correct answer.

Question

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 h is the height of the balloons after m minutes, determine which system of equations represents this situation.

A.
h = 3,000 + 40m
h = 1,200 - 50m
B.
h = 3,000 - 40m
h = 1,200 + 50m
C.
h = 3,000m - 40
h = 1,200m + 50
D.
m = 3,000 - 40h
m = 1,200 + 50h

Answer 1

To represent the situation accurately, we need to model the height of each balloon as a function of time (in minutes).

1. First Balloon:

   • It starts at a height of 3,000 feet and decreases in height at a rate of 40 feet per minute.
   • Therefore, its height after \( m \) minutes can be modeled as: \[ h = 3,000 - 40m \]

2. Second Balloon:

   • It starts at a height of 1,200 feet and rises at a rate of 50 feet per minute.
   • Therefore, its height after \( m \) minutes can be modeled as: \[ h = 1,200 + 50m \]

Combining both equations, we can conclude that the correct system of equations representing this situation is:

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