Chapter 8.4, Problem 38E

To determine

Which trail should the instructor take? Explain.

Answer to Problem 38E

The instructor should take trail A.

Explanation of Solution

Given:

A riding instructor takes students to mountain trials. The instructor wants to avoid steep trials. One the steepestpart of trail A, the path rises 15 feet over a horizontal distance of 50 feet. One the steepest part of trail B, the path rises 30 feet over a horizontal distance of 75 feet.

Calculation:

We will use slope formula to solve our given problem.

  $\text{Slope}=\frac{\text{Rise}}{\text{Run}}$

Let us find slope of both trails one by one.

  $\text{Slope of trail A}=\frac{15}{50}=0.3$

The slope of path along trial A is 0.3 feet.

  $\text{Slope of trail B}=\frac{30}{75}=0.4$

The slope of path along trial A is 0.3 feet.

Since the slope of trail B is greater than slope of trail A, so the path along trail B is steepest. Therefore, the instructor should take trail A.