Chapter 8.1, Problem 42IP

(a)

To determine

How long will it take her to hike the Lone Star Trail

Answer to Problem 42IP

It take her to time is $1.92h$

Explanation of Solution

Given:

Jenna hikes at a steady rate of 2.5 miles per hours

  

Concept Used:

  $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find how long it take her to hike the Lone Star Trail

Lone Star Trail Round Trip Distance is $4.8miles$

Let x be the time then $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Then the time is below:

  $\begin{array}{l}2.5x=4.8\\ \frac{2.5x}{2.5}=\frac{4.8}{2.5}\\ x=1.92\end{array}$

Thus, the time is $1.92h$

(b)

To determine

His average hiking rate

Answer to Problem 42IP

The average hiking rate is $1.7mil/h$ .

Explanation of Solution

Given:

It takes Ming 4 hours to hike the Mallard Lake Trail

Concept Used:

  $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the average rate is below:

  $\begin{array}{l}Dis\tan ce=6.8\\ Time=4hour\\ Speed=x\\ \text{Speed}=\frac{\text{Distance}}{\text{Time}}\\ x=\frac{6.8}{4}\\ x=1.7\end{array}$

Thus, the average hiking rate is $1.7mil/h$ .

(c)

To determine

The round trip distance of Mystic Fall Trail

Answer to Problem 42IP

The round trip distance of the Mystic Fall Trail is $2.5mi$ .

Explanation of Solution

Given:

The round trip distance of the Observation Point Trail is 56%

Concept Used:

  $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the round trip distance of the Mystic Fall Trail is below:

  $\begin{array}{l}0.56x=1.4\\ \frac{0.56x}{0.56}=\frac{1.4}{0.56}\\ x=2.5mi\end{array}$

Thus, the round trip distance of the Mystic Fall Trail is $2.5mi$ .