Chapter 6.2, Problem 23PPS

a.

To determine

To calculate:Each person’s Speed as unit Rate.

Answer to Problem 23PPS

  ${\text{S}}_{\text{A}}=8{\text{ f t /sec and S}}_{\text{J}}=6\text{ f t}/\sec$

Explanation of Solution

Given information:

A line graph which shows average rates in a race. $x-\text{axis}$ represents time in seconds and $y-\text{axis}$ represents distance travelled.

  

Speed as Unit Rate: Speed as unit rate is the term used to describe the change in speed per unit time. In general, we can say that the distance travelled in each second or in one second.

Consider the given graph as,

  

From the given graph, it is clear that

  $\begin{array}{c}{\text{S}}_{\text{A}}=8\text{ f t /sec}\\ {\text{S}}_{\text{J}}=\frac{12}{2}\text{ f t / sec}\\ =6\text{ f t}/\sec \end{array}$

b.

To determine

To calculate: The time required by the person A and the person J to run 1 mile.

Answer to Problem 23PPS

  $T_A=11\text{ hrs and }{T}_j=14.66\text{ hrs}$

Explanation of Solution

Given information:

  ${\text{S}}_{\text{A}}=8ft/\sec {\text{ and S}}_{\text{j}}=6ft/\sec$

A line graph which shows average rates in a race. $x-\text{axis}$ represents time in seconds and $y-\text{axis}$ represents distance travelled.

  

Formula Used:

  $\text{One mile }=5280\text{ feet}$

Calculation:

Since, ${\text{S}}_{\text{A}}=8\text{ f t / sec}$

That means distance travelled in 1 sec is 8 ft.

Then, required time $T_A=\frac{5280}{8}=660\sec \text{ or }11\text{hrs}$

Similarly, ${\text{S}}_{\text{j}}=6\text{ f t / sec}$

That means distance travelled in 1 sec is 6 ft.

Then, required time $T_j=\frac{5280}{6}=880\sec \text{ or }14.66\text{ hrs}$

Therefore, $T_A=11\text{ hrs and }{T}_j=14.66\text{ hrs}$

c.

To determine

To graph: The line representing his speed would be graphed,if the max running rate is 5 feet per second.

Explanation of Solution

Given information:

  ${\text{S}}_{\text{A}}=8ft/\sec {\text{ and S}}_{\text{j}}=6ft/\sec$

A line graph which shows average rates in a race. $x-\text{axis}$ represents time in seconds and $y-\text{axis}$ represents distance travelled.

  

Since the person J speed is 6 ft per second and the person M’s speed is 5 ft per second. The line representing the speed of the person M will be below the line for the speed of the person J.