Chapter 9.6, Problem 19E

a.

To determine

To find the distance between one corner to opposite corner of a square in diagonally.

Answer to Problem 19E

The distance between one corner to opposite corner of a square in diagonally $=113ft$

Explanation of Solution

Given:

  

Calculation:

The distance between $A$ and $C$

= $\begin{array}{l}d=\sqrt{{800}^2+{800}^2}\\ =\sqrt{640000+640000}\\ =\sqrt{1280000}\\ =1131.4\\ \approx 1131ft\end{array}$

b.

To determine

To find the rate of $3$ miles per hour in foot per second.

Answer to Problem 19E

The rate of $3$ miles per hour= $4.4\text{ foot / sec}$

Explanation of Solution

Given: Rate $3$ in miles per hour.

Calculation:

The rate of $3$ miles per hour is obtained as follows:

  $\begin{array}{l}\text{1 mile = 5280 foot}\\ \text{1 hour = 3600 seconds}\end{array}$

Substitute in above equation to find the rate of $3$ miles per hour is, $\frac{3miles}{hour}=\frac{3\ast 5280\text{ foot}}{3600\text{ seconds}}=4.4\text{ foot per second}\text{.}$

Hence, the rate of $3$ miles per hour= $4.4\text{ foot / sec}$

c.

To determine

To find the time save by walking along the diagonal rather than walking along two sides of the square.

Answer to Problem 19E

Time saved by walking along the diagonal rather than walking along two sides of the square $=106.5\text{ seconds}$ .

Explanation of Solution

Given:

  

Calculation:

The time taken to walk along the diagonal is calculated as the distance travelled divided by the speed = $\frac{1131.4}{4.4}=257.14$ seconds.

The time taken to walk across the two sides of the square is calculated as the distance travelled by the speed = $\frac{2\ast 800}{4.4}=363.64\text{seconds}$

Hence, the time difference between the above two conditions = $363.64-257.14=106.5$ seconds.

That means, time saved by walking along the diagonal rather than walking along two sides of the square $=106.5\text{ seconds}$ .