# Hot Air Balloon

## Hot Air Balloon

At the West Texas Balloon Festival, a hot-air balloon is sighted at an altitude of 800 feet and appears to be descending at a steady rate of 20 feet per minute. Spectators are wondering how the altitude of the balloon is changing as time passes

What function relating the variables best describes this situation?

f(x)= 800-20x

Make a table of values and a graph to show the balloon’s altitude every 5 minutes beginning at 5 minutes before the balloon was sighted until the balloon lands.

How high was the balloon 5 minutes before it was sighted? Show graph and explain.

The balloon was 900ft up in the air before it was sighted.

How long does it take the balloon to reach an altitude of 20 feet? How long does it take the balloon to land? Show graph and explain.

39 minutes to get an altitude of 20 ft, and 40 minutes to land.

A second balloon is first sighted at an altitude of 1200 feet but is descending at 20 feet per minute. Write the function that represents this situation. How much longer does it take for the second balloon to land compared with that of the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines.

F(x)= 1200-20x, it takes this balloon 20 minutes longer to reach the ground than the first balloon. (60 minutes)

A third balloon is first sighted at an altitude of 800 feet but is descending at 30 feet per minute. Write the function that represents this situation. How much longer does it take for the third balloon to land compared with that of the first balloon? How does the descent of the balloons compare? Show the graph. Explain the relationship between the two lines.

F(x)= 800-30x, This balloon will reach the ground 13.33 minutes before the first balloon. The first balloon is 10 ft/m slower than this one.

At the instant the first balloon is sighted, a fourth balloon is launched from the ground rising at a rate of 30 feet per minute. Write the function that represents this situation.

When will the first and fourth balloon be at the same altitude? What is that altitude? Show the graph. What does this mean graphically?

F(x)= 30x, The first and fourth balloon will be at the same altitude in 16 minutes, and the altitude will be 480ft.

At what altitude would the 3rd balloon have to begin its descent in order to reach the ground at the same time as the 1st balloon? What is the equation of the line?

The altitude it would have to start at would be 1200ft. F(x)= 1200 - 30x