Chapter 1, Problem 1.51QP

(a)

Interpretation Introduction

Interpretation: The average speed of woman in miles per hour and in meters per second is to be calculated.

Concept introduction: Speed is the ratio of distance covered and time taken.

To determine: The average speed of woman in miles per hour.

Answer to Problem 1.51QP

Solution

The average speed of woman in miles per hour is $\underset{\_}{7.35miles/hour}$.

Explanation of Solution

Explanation

Given

The distance is $\text{26}\text{.2}\text{miles}$.

Time is $3$ hours and $34$ minutes.

The conversion of minutes to hours is done as,

$1\text{minute}=\frac{1}{60}\text{hours}$

Therefore, the conversion $34$ minutes to hours is done as,

$\begin{array}{c}34\text{minute}=\frac{34}{60}\text{hours}\\ =\text{0}\text{.56}\text{hours}\end{array}$

Therefore, the time in hours is $\text{3}+\text{0}\text{.56}\text{hours}=3.56\text{hours}$.

The average speed of woman in miles per hour is calculated by the formula,

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

Substitute the value of distance and time in the above equation.

$\begin{array}{c}\text{Speed}=\frac{\text{26}\text{.2}\text{miles}}{3.56\text{hours}}\\ =\underset{\_}{7.35miles/hour}\end{array}$

(b)

Interpretation Introduction

To determine: The average speed of woman in meters per second.

Answer to Problem 1.51QP

Solution

The average speed of woman in meters per second is $\underset{\_}{3.29metres/\sec ond}$.

Explanation of Solution

Explanation

Given

The distance is $\text{26}\text{.2}\text{miles}$.

Time is $3$ hours and $34$ minutes.

The conversion of miles to meters is done as,

$\text{1}\text{mile}=1609.34\text{metre}$

Therefore the conversion of $\text{26}\text{.2}\text{miles}$ to meters is done as,

$\begin{array}{c}26.2\text{mile}=26.2\times 1609.34\text{metres}\\ =\text{42164}\text{.708}\text{metres}\end{array}$

The conversion of minutes to hours is done as,

$1\text{minute}=\frac{1}{60}\text{hours}$

Therefore, the conversion $34$ minutes to hours is done as,

$\begin{array}{c}34\text{minute}=\frac{34}{60}\text{hours}\\ =\text{0}\text{.56}\text{hours}\end{array}$

Therefore, the time in hours is $\text{3}+\text{0}\text{.56}\text{hours}=3.56\text{hours}$.

The conversion of hours to seconds is done as,

$1\text{hour}=3600\text{seconds}$

Therefore, the conversion $3.56\text{hours}$ to seconds is done as,

$\begin{array}{c}3.56\text{hour}=3.56\times 3600\text{seconds}\\ \text{=12816}\text{seconds}\end{array}$

Therefore, the time in seconds is $\text{12816}\text{seconds}$.

The average speed of woman in miles per hour is calculated by the formula,

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

Substitute the value of distance and time in the above equation.

$\begin{array}{c}\text{Speed}=\frac{\text{42164}\text{.708}\text{metres}}{\text{12816}\text{seconds}}\\ =\underset{\_}{3.29metres/\sec ond}\end{array}$

The average speed of woman in meters per second is $\underset{\_}{3.29metres/\sec ond}$.

Conclusion

The average speed of woman in meters per second is $\underset{\_}{3.29metres/\sec ond}$