JakeCassidy15
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Hot Air Balloon 1 is 10 meters above the ground, rising 15 meters per minute, and Hot Air Balloon 2 is 150 meters above the ground descending 20 meters per minute.
In how many minutes will the balloons be at the same height?
How high will the balloons be at that time?
(Let x represent the time and y represent the height)

Sagot :

eternal3fear
You have two equations
y = 10 + 15x   and    y = 150 - 20x
since  y = y   you can get
10 + 15x = 150 - 20x    now we solve for x
      +20x         +20x     add 20x to both sides
10 + 35x = 150    now subtract 10 from both sides
-10             -10
35x = 140    then divide both sides by 35
/35      /35
so  x = 4 minutes

to find what high they are at 4 minutes
plug 4 back into the equation for x
y = 10 + 15(4) = 10 + 60 = 70
so  70 meters from the ground

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

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