Chapter 8.8, Problem 49IP

To determine

Find nearest hundredth, by now how many miles she should increase her daily run to meet her goal.

Answer to Problem 49IP

4.73 miles

Explanation of Solution

Given:

A good rule to know when training for a marathon is that you will generally have enough endurance to finish a race that is 3 times your average daily distance. Tammy wants to be able to run at least the standard marathon distance of 26.2 miles. The length of her current daily run is about 4 miles. To the nearest hundredth, by how many miles should she increase her daily run to meet her goal?

Concept Used:

Let d be represents the daily miles she should increase her daily.

The length of her current daily run is about 4 miles. After the increase of d miles it would be (4+ d ) miles.

The required inequality: $3(4+d)\ge 26.2$

Calculation:

The required inequality: $3(4+d)\ge 26.2$

Solve for d :

  $\begin{array}{l}3(4+d)\ge 26.2\\ 12+3d\ge 26.2\\ 12-12+3d\ge 26.2-12[\text{Subtract}\text{12}\text{from}\text{both}\text{sides}]\\ 3d\ge 14.2\\ \frac{3d}{3}\ge \frac{14.2}{3}[\text{Divide}\text{each}\text{side}\text{by}3]\\ d\ge 4.73\end{array}$

Thus, she has to increase her daily run by 4.73 miles.