Question 309286
Plane is traveling at 210 miles per hour.

Divide 210 by 60 and you get 3.5 miles per minute.

The plane takes 6 minutes to land.

This means that in 6 minutes, the plane will drop from an altitude of 1.3 miles to an altitude of 0.

This means that the plane is dropping (1.3/6) miles per minute.


Since the plane's speed is 3.5 miles per minute, this means that the plane is dropping (1.3/(6*3.5)) miles of altitude per miles of distance from the airport.


The equation for the rise in altitude is equal to:


y = ((1.3)/(6*3.5))* x


A graph of this equation looks like this:


{{{graph(600,600,-2,22,-1,2,(1.3/(6*3.5))*x,1.3)}}}


I needed to use a rise in altitude rather than a drop in altitude because you wanted the y-axis to reflect the altitude and the x-axis to reflect the distance from the airport.


You read the graph as follows:


y is the altitude of the plane.
x is the distance from the airport.


When x = 0, the altitude is 0 because the plane has landed.


When x = 21 miles form the airport, the altitude is 1.3 miles high.


You can see that by tracing a vertical line from the intersection of the equation of the plane's altitude with the line at y = 1.3 miles to see that the intersection occurs at about x = 21.


To determine the distance from the airport when the altitude is 1.1 miles, you would calculate the equation when y = 1.1


The equation is y = ((1.3)/(6*3.5))*x


Set y equal to 1.1 to get:

1.1 = ((1.3)/(6*3.5))*x

Solve for x to get:


x = (1.1*6*3.5)/(1.3) which becomes:


x = 17.769230977


The altitude of the plane is 1.1 miles when the plane is 17.769230977 miles from the airport.


The graph is shown again below with a horizontal line at y = 1.1.


{{{graph(600,600,-2,22,-1,2,(1.3/(6*3.5))*x,1.3,1.1)}}}


Trace a vertical line from the intersection of this line with the graph of the equation of the plane's altitude to see that the value of x is somewhere around 17.8 when this occurs, as it should.