Chapter 2.3, Problem 38E

To determine

To calculate:

The inequality equation and solution that represents the possible distance travelled by beginner

Answer to Problem 38E

The inequality equation and solution that represents the possible distance travelled by beginner is $\frac{d}{t}\ge 18$ and $d\ge 13.5miles$ receptively.

Explanation of Solution

Given information:

Speed is less than $18mph$

Travel time: $45\min$

Formula used:

The speed is expressed as:

  $S=\frac{d}{t}$

Where,

Distance: $d$

Time: $t$

Calculation:

Consider,

Possible miles can be travelled by beginner: $d$

Know that: speed is less than $18mph$

  $S\le 18mph$  .. . . . (1)

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

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

  $\begin{array}{l}S\ge 18mph\\ \frac{d}{t}\ge 18\end{array}$

So, the inequality equation that represents possible miles to travel is $\frac{d}{t}\ge 18$ .

The solution of $\frac{d}{t}\ge 18$ is:

  $\begin{array}{l}\frac{d}{t}\ge 18\\ \frac{d}{45}\ge 18\end{array}$

Multiply by $45$ on both sides of the above equations:

  $\begin{array}{l}\frac{d}{45}\times 45\ge 18\times 45\\ d\ge \frac{27}{2}\\ d\ge 13.5miles\end{array}$