Question

The grade of a road is its slope written as a percent. A warningsign must be posted if a section of road has a grade of at least 8% and ismore than 750 feet long.a. Interpret and Apply A road rises 63 feet over a horizontal distanceof 840 feet. Should a warning sign be posted? Explain your thinking.b. Critical Thinking The grade of a section of road that stretches over ahorizontal distance of 1000 feet is 9%. How many feet does the roadrise over that distance?

Answer 1

(a)Grade =7.5% (No warning sign is needed)

(b)Rise =90 feet

Explanation:

`\text{Slope = }(Rise)/(Run)`

(a)

Rise = 63 feet

Run (Horizontal distance) = 840 feet.

`\text{Slope = }(63)/(840)=0.075\\\\$Grade=Slope * 100 = 0.075 * 100 = 7.5\%`

A warning sign should not be posted since its grade is less than 8%.

(b)

Grade = 9%

Run (Horizontal distance) = 1000 feet.

Recall that:

Grade = Slope X 100

`9 =(Rise)/(1000) * 100\\\\9 =(Rise)/(10)\\\\$Rise = 9 * 10 \\$Rise=90 feet`

The road rises 90 feet over a distance of 1000 feet.