Mathematics, 11.10.2019 22:10 acediego3119

Ared balloon is 40 feet above the ground and rising at 2ft/s at the same time a blue balloon is at 60 feet above the ground and descending at 3ft/s what will the height of the balloons be when they are the same height above the ground

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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:

$r \to$ rate

$h \to$ height

$t \to$ time

For the red balloon, we have:

h_0 = 40 --- the initial height

r = 2 --- the rate

For the blue balloon, we have:

h_0 = 60 --- the initial height

r = -3 --- the rate (it is negative because the balloon is descending)

The equation to represent the height of both balloon is:

h = h_0 + rt

So, we have:

h = 40 + 2t --- the position of the red balloon

h = 60 - 3t --- the position of the blue balloon

Both balloons will be at the same height, when:

h = h

So, we have:

40 + 2t = 60 -3t

Collect like terms

2t + 3t = 60 -40

5t = 20

Divide both sides by 5

t = 4

Calculate the height

Substitute 4 for t in h = 60 - 3t

$h =60 - 3 \times 4$

h =60 - 12

h = 48

Hence, the balloons will be at the same height above the ground at 48ft

Read more about linear equations at:

link

Answer from: babymom74

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.

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")

time = distance/speed

distance = speed × time

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

Answer from: Quest

idk

step-by-step explanation:

use that smart brain

Answer from: Quest

the answer is 48m^2!

step-by-step explanation:

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