Question

Your hot air balloon is rising at the rate of 4 feet per second. Another aircraft nearby is at 7452 feet and is losing altitude at the rate of 30 feet per second. In how many seconds will your hot air balloon be at the same altitude as the other aircraft?​

Answer 1

`219.2\ sec`

Explanation:

Let

y ----> the altitude in feet

x ----> the time in seconds

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope ot unit rate

b is the y-intercept or initial value

In this problem we have

Your hot air balloon

The slope is equal to
`m=4\ (ft)/(sec)`

The y-intercept is
`b=0` ---> represent a proportional relationship

The linear equation is

`y=4x` ----> equation B

Another aircraft

The slope is equal to
`m=-30\ (ft)/(sec)` ---> is negative because is a decreasing function

The y-intercept is
`b=7,452\ ft`

The linear equation is

`y=-30x+7,452` ----> equation B

Equate equation A and equation B

`4x=-30x+7,452`

solve for x

Adds 30x both sides

`4x+30x=7,452`

`34x=7,452`

Divide by 34 both sides

`x=219.2\ sec`