The time at which the ballons are at the same height is 4 minutes and the height of the ballons at that time is 70 meters and this can be determined by using the given data.
Given :
- Hot Air Balloon 1 is 10 meters above the ground, rising 15 meters per minute.
- Hot Air Balloon 2 is 150 meters above the ground descending 20 meters per minute.
The following steps can be used in order to determine the time in minutes at which the balloons be at the same height and also the height of the ballons:
Step 1 - The height of balloon 1 from the ground is:
[tex]H_1= 10+15t[/tex]
where 't' is the time.
Step 2 - The height of balloon 2 from the ground is:
[tex]H_2= 150-20t[/tex]
where 't' is the time.
Step 3 - So, the time at which the ballons are at the same height is calculated as:
[tex]\begin{aligned}\\15t +10&=150-20t\\35t &= 140\\t& = 4\;{\rm minutes}\\\end{aligned}[/tex]
Step 4 - So, the height of the ballons at (t = 4) is:
[tex]{\rm Height} = 10+15\times (4)[/tex]
[tex]{\rm Height} = 70\;{\rm meters}[/tex]
The time at which the ballons are at the same height is 4 minutes and the height of the ballons at that time is 70 meters.
For more information, refer to the link given below:
https://brainly.com/question/10726356
