Chapter 2.3, Problem 31E

a.

To determine

To calculate:

The inequality equation and solution that represents possible numbers of miles to run

Answer to Problem 31E

The inequality equation that represents possible numbers of miles to run is $\frac{d}{2}\le 6.3$ and its solution is $d\le 12.6$

Explanation of Solution

Given information:

Time: $2hrs$

Speed: faster than $6.3mph$

Formula used:

The speed is expressed as:

  $S=\frac{d}{t}$

Where,

Distance: $d$

Time: $t$

Calculation:

Consider,

Number of miles to run: $d$

Know that: speed is faster than $6.3mph$

  $S\ge 6.3mph$  .. . . . (1)

Now, need to write the inequality equation that represents possible numbers of miles to run that means in terms of $d$ :

Put $S=\frac{d}{t}$ in eq. (1):

  $\begin{array}{l}S\le 6.3mph\\ \frac{d}{t}\le 6.3\\ \frac{d}{2}\le 6.3\end{array}$

Multiply by $2$ on both sides of the above equations:

  $\begin{array}{l}\frac{d}{2}\le 6.3\\ \frac{d}{2}\times 2\le 6.3\times 2\\ d\le 2\left(6.3\right)\\ d\le 12.6\end{array}$

b.

To determine

To explain:

The judgment pass by friend is correct o not

Answer to Problem 31E

Yes, friend’s is correct as the person cannot complete Marathon $26.2mile$ within $4hrs$ of time limit. Person can complete the Marathon in $4.16hrs$ .

Explanation of Solution

The marathon is approximately of $26.2mile$ . The friend said that person cannot complete it within $4hrs$ of time limit. Need to justify the friend’s judgement is correct or not.

Consider,

Number of hours that person run: $thrs$

Use the speed formula here:

  $S=\frac{d}{t}$

Know that: $d=26.2mile,S=6.3mph$

  $\begin{array}{l}S=\frac{d}{t}\\ 6.3=\frac{26.2}{t}\\ t=\frac{26.2}{6.3}\\ t\approx 4.16hrs\end{array}$

That means the person can complete the Marathon $26.2mile$ in $4.16hrs$ . So, the friend’s is correct as the person cannot complete Marathon $26.2mile$ within $4hrs$ of time limit.