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

Answers: 1

Show answers

Answers

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

29.5977692753

step-by-step explanation:

Answer from: Quest

For being nice i appreciate it but abc

Another question on Mathematics

Mathematics, 21.06.2019 15:20

Which equation represents a circle with a center at (–3, –5) and a radius of 6 units? (x – 3)2 + (y – 5)2 = 6 (x – 3)2 + (y – 5)2 = 36 (x + 3)2 + (y + 5)2 = 6 (x + 3)2 + (y + 5)2 = 36

Answers: 3

Answer

Mathematics, 21.06.2019 16:00

Sam makes his sales calls according to a pattern. he travels either north or south depending on the calendar. some of his past trips were as follows: on february 17, april 24, june 10, september 19, and november 3 he drove north. on february 28, may 25, august 22, november 20, and december 18, he drove south. describe sams' pattern. in which direction will sam drive on oct4 and oct 24?

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Plot the intercepts to graph the equation

Answers: 1

Answer

Mathematics, 21.06.2019 22:50

Use the quadratic function to predict f(x) if x equals 8. f(x) = 25x2 − 28x + 585

Answers: 1

Answer

You know the right answer?

Ared balloon is 40 feet above the ground and rising at 2ft/s at the same time a blue balloon is at 6...