Question

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?

Answer 1

recall that, there are 12 inches in 1 foot, now, when the ramp is 4 feet away, that's 4*12 inches, and when it's 6 feet away, that's 6*12 inches.


`\bf \begin{array}{ccll} \stackrel{\textit{inches from driveway}}{x}&\stackrel{\textit{inches of ramp's height}}{y}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 48&12\\ 72&18 \end{array}\\\\ -------------------------------`

Answer 2

The rate of change of the ramp's incline is 3 inches up per foot across.

Explanation:

Given,

At a point 4 feet from the driveway, the height of the ramp is 12 inches,

The position of a point on ramp = (4,12),

Also, At a point 6 feet from the driveway, the height of the ramp is 18 inches.

The position of another point on the ramp = (6,18),

After making the diagram,

The rate of change of the ramp’s incline =
`(18-12)/(6-4)`

`=(6)/(2)`

`=3\text{ inches up per foot across}`