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

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:

rate

height

time

For the red balloon, we have:

--- the initial height

--- the rate

For the blue balloon, we have:

--- the initial height

--- the rate (it is negative because the balloon is descending)

The equation to represent the height of both balloon is:

So, we have:

--- the position of the red balloon

--- the position of the blue balloon

Both balloons will be at the same height, when:

So, we have:

Collect like terms

Divide both sides by 5

Calculate the height

Substitute 4 for t in

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

Read more about linear equations at:

link

  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")

or

  time = distance/speed

or

  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

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

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