Chapter 11.4, Problem 33PPE

a.

To determine

The expression that represent the total time Jane spends walking.

Answer to Problem 33PPE

  $\frac{1}{r}+\frac{1}{0.7r}$

Explanation of Solution

Given information:

Jane walks one mile from her house to her grandparents’ house. Ten she returns home walking with her grandfather. Her return rate is 70% of her rate walking alone.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the speed of Jane walking alone be r miles per hour. So, the speed returning back would be $0.7r$ as it is 70% of her rate walking alone.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time walking alone + Time returning back}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed going out}}+\frac{\text{Distance traveled}}{\text{Speed returning back}}\\ =\frac{1}{r}+\frac{1}{0.7r}\end{array}$

Thus, the expression for total time is $\frac{1}{r}+\frac{1}{0.7r}$ .

b.

To determine

Simplify the expression from part (a).

Answer to Problem 33PPE

  $\frac{17}{7r}$

Explanation of Solution

Given information:

Jane walks one mile from her house to her grandparents’ house. Ten she returns home walking with her grandfather. Her return rate is 70% of her rate walking alone.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the speed of Jane walking alone be r miles per hour. So, the speed returning back would be $0.7r$ as it is 70% of her rate walking alone.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time walking alone + Time returning back}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed going out}}+\frac{\text{Distance traveled}}{\text{Speed returning back}}\\ =\frac{1}{r}+\frac{1}{0.7r}\\ =\frac{0.7}{0.7r}+\frac{1}{0.7r}\\ =\frac{0.7+1}{0.7r}\\ =\frac{1.7}{0.7r}\\ =\frac{17}{7r}\end{array}$

Thus, the expression for total time is $\frac{17}{7r}$ .

c.

To determine

How much time does Jane spend walking if her rate of walking alone is 3 mi/h.

Answer to Problem 33PPE

  $0.81\text{ hours}\approx 49\text{ minutes}$

Explanation of Solution

Given information:

Jane walks one mile from her house to her grandparents’ house. Ten she returns home walking with her grandfather. Her return rate is 70% of her rate walking alone.

Concept used:

The formula for the distance traveled is $d=rt$

Calculation:

Let the speed of Jane walking alone be r miles per hour. So, the speed returning back would be $0.7r$ as it is 70% of her rate walking alone.

Now in order to find the expression that represents the total time, use the time-distance formula with the given values as shown below

  $\begin{array}{c}\text{Total time}=\text{Time walking alone + Time returning back}\\ \text{=}\frac{\text{Distance traveled}}{\text{Speed going out}}+\frac{\text{Distance traveled}}{\text{Speed returning back}}\\ =\frac{1}{r}+\frac{1}{0.7r}\\ =\frac{0.7}{0.7r}+\frac{1}{0.7r}\\ =\frac{0.7+1}{0.7r}\\ =\frac{1.7}{0.7r}\\ =\frac{17}{7r}\end{array}$

Now since her rate of walking alone is $r=3$ , so the time taken would be

  $\begin{array}{c}\frac{17}{7r}=\frac{17}{7\left(3\right)}\\ =\frac{17}{21}\\ \approx 0.81\text{ hours}\\ \approx 49\text{ minutes}\end{array}$

Thus, the time spend walking is approximately $0.81\text{ hours}\approx 49\text{ minutes}$ .