Chapter 8.4, Problem 37E

a.

To determine

A road rises 63 feet over a horizontal distance of 840 feet. Should a warning sign be posted? Explain your reasoning in your answer.

Answer to Problem 37E

The warning sign is not required.

Explanation of Solution

Given:

The grade of a road is its slope written as percentage. A warning sign must be posted if a section of road has a grade of at-least 8% and is more than 750 feet long.

Calculation:

We can see that horizontal distance is 840 feet, which is greater than 750 feet.

Now we will use slope formula to find grade of road as:

  $\begin{array}{l}\text{Slope}=\frac{\text{Rise}}{\text{Run}}\\ \text{Slope}=\frac{63}{840}\\ \text{Slope}=0.075\end{array}$

Now, we will convert slope as a percent by multiplying 0.075 by 100.

  $0.075\times 100=7.5\%$

Since the grade of road is 7.5%, which is less than 8%, therefore, the warning sign is not required.

b.

To determine

To find:

How many feet does the road rise over the given distance?

Answer to Problem 37E

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

Explanation of Solution

Given:

The grade of a road is its slope written as percentage. A warning sign must be posted if a section of road has a grade of at-least 8% and is more than 750 feet long.

The grade of a section of road that stretches over a horizontal distance of 1000 feet is 9%.

Calculation:

We will use slope formula to solve our problem as:

  $\begin{array}{l}\text{Slope}=\frac{\text{Rise}}{\text{Run}}\\ \text{9\%}=\frac{\text{Rise}}{1000}\\ \frac{\text{9}}{100}=\frac{\text{Rise}}{1000}\\ \frac{\text{9}}{100}\cdot 1000=\frac{\text{Rise}}{1000}\cdot 1000\\ 90=\text{Rise}\end{array}$

Therefore, the road rises 90 feet over a horizontal distance of 1000 feet.