Chapter 2.4, Problem 38E

To determine

An inequality to show how the runner can achieve his goal of having average running time of less than $24$ minutes.

Explanation of Solution

Given information:

The runners time in the four races he has completed are $25.5,24.3,24.8and24.8$ .

The runner plans to run one more race.

Calculations:

Total time taken by the runner in completing the race four times is

  $25.5+24.3+24.8\text{ + }23.5=98.1$

Let the time taken by the fifth race be $x$ .

Therefore total time taken for the five race is = $98.1+x$

Now average time for the five races is,

  $\text{Average time}=\frac{98.1+x}{5}$

Now for average time less than $24$ minutes, we can write,

  $\frac{98.1+x}{5}<24$

Now solving the inequality we can get the time taken for the fifth race,

  $\begin{array}{l}\frac{98.1+x}{5}<24\\ 98.1+x<24\times 5\\ 98.1+x<120\\ x<120-98.1\\ x<21.9\end{array}$

Thus the time for the fifth race should be less than $21.9$ for getting average time of $24$ minutes.