HotAir Balloons
BY: JADE N
At the West Texas Balloon Festival, a hotair 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. (Balloon #1)
Here is a table that shows Balloon #1's altitude every 5 minutes beginning 5 minutes before the balloon was sighted:
Here is a graph of Balloon #1 five minutes before it was sighted:
900 feet
The red circle on the graph shows the point of how high the balloon was 5 minutes before being sighted.
Here is a graph of how long it will take Balloon #1 to reach an altitude of 20 feet and how long it takes it to land:
Y=20x+800= 39 minutes (to reach 20 feet)
40 minutes to land
The green circle on the graph represents where the hotair balloon is at about 20 feet. The red circle on the graph shows when the hotair balloon lands.
A second balloon is first sighted at an altitude of 1200 feet but is descending at 20 feet per minute. (Balloon #2)
Y= 120020x
Here is a graph that shows how much longer it takes for Balloon #1 to land verses Balloon #2 and the relationship between the two balloons:
The red circles represent when the balloons have landed. The descent of the balloons are similar in that they both descend at 20 feet per minute. Balloon #1 reaches the ground after 40 minutes and Balloon#2 reaches the ground after 60 minutes.
A third balloon is first sighted at an altitude of 800 feet but is descending at 30 feet per minute. (Balloon #3)
Y= 80030x
Here is a graph that shows how much longer it takes Balloon #3 to land compared to Balloon #1 and how they compare:

The red circles on the graph indicate when the balloons reached the ground. It takes Balloon#1 about 10 more minutes to reach the ground than Balloon #3. The rate of descent of Balloon#3 is faster by 10 feet per minute than Balloon #1.
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. (Balloon #4)
This function represents the situation:
Y1= 20x+800 Y4= 30x Y1=Y4 Function: 30x=20x+800
Here is a graph that shows when Balloon #1 and Balloon #4 will be at the same altitude:
The red circle on the graph represents where Balloon #1 and Balloon #4 intersect. This intersection occurs after 16 minutes of Balloon #1 descending and Balloon #4 rising and the altitude is about 500 feet.
Spectators are wondering what altitude Balloon #3 has to begin its descent in order to reach the ground the same time as Balloon #1. Here is the answer:
Balloon #3 would have to start descending at 1,200 feet in the air.
Here is a graph to display the information:
20x+800=30x+1200