Answer:
48 ft
Step-by-step explanation:
The height gap between the balloons is 60 -40 = 20 feet. That gap is being closed at the rate of 2 + 3 = 5 ft/s, so will be gone in ...
(20 ft)/(5 ft/s) = 4 s
At that time, the red balloon will have risen (2 ft/s)(4 s) = 8 ft to a height of ...
40 ft +8 ft = 48 ft
The blue balloon will have descended (3 ft/s)(4 s) = 12 ft to a height of ...
60 ft -12 ft = 48 ft
The balloons at at 48 ft when they are both the same height.
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Time and speed and distance are related by the formula you see on every speed limit sign:
speed = distance/time . . . . . . . (on the sign, it's "miles per hour")
or
time = distance/speed
or
distance = speed × time
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If you want equations, you can write them as ...
h = 40 +2t
h = 60 -3t
where h is the altitude the balloons have when they are at the same height, and t is the number of seconds it takes to get there.
We're only interested in h, so we can cancel t by multiplying the first equation by 3 and adding that to the second equation multiplied by 2:
3(h) + 2(h) = 3(40 +2t) +2(60 -3t)
5h = 120 +6t +120 -6t
h = 240/5 = 48 . . . . the height in feet at which the balloons are the same height
The height of both balloon relative to time is an illustration of a linear equation. The balloons will be at the same height at 48 feet.
Let:
[tex]r \to[/tex] rate
[tex]h \to[/tex] height
[tex]t \to[/tex] time
For the red balloon, we have:
[tex]h_0 = 40[/tex] --- the initial height
[tex]r = 2[/tex] --- the rate
For the blue balloon, we have:
[tex]h_0 = 60[/tex] --- the initial height
[tex]r = -3[/tex] --- the rate (it is negative because the balloon is descending)
The equation to represent the height of both balloon is:
[tex]h = h_0 + rt[/tex]
So, we have:
[tex]h = 40 + 2t[/tex] --- the position of the red balloon
[tex]h = 60 - 3t[/tex] --- the position of the blue balloon
Both balloons will be at the same height, when:
[tex]h = h[/tex]
So, we have:
[tex]40 + 2t = 60 -3t[/tex]
Collect like terms
[tex]2t + 3t = 60 -40[/tex]
[tex]5t = 20[/tex]
Divide both sides by 5
[tex]t = 4[/tex]
Calculate the height
Substitute 4 for t in [tex]h = 60 - 3t[/tex]
[tex]h =60 - 3 \times 4[/tex]
[tex]h =60 - 12[/tex]
[tex]h = 48[/tex]
Hence, the balloons will be at the same height above the ground at 48ft
Read more about linear equations at:
https://brainly.com/question/2263981
