Chapter 11.4, Problem 4LC

To determine

To write the expression for time spent on running up and down the hill by the runner.

Answer to Problem 4LC

  $\frac{2}{r}+\frac{4}{r}$

Explanation of Solution

Given:

The runner practice running 2 mile up given slope and 2 miles down, and speed of the running down is 50% faster than the speed of running up.

Concept Used:

  $\text{Time}=\frac{\text{distance}}{\text{Speed}}$

Calculation:

To write the expression for time spent on running up and down the hill by the runner use the formula

  $\text{Time}=\frac{\text{distance}}{\text{Speed}}$

First consider the runner’s speed when running up the slope is r miles per hour, and since it is 50% faster that means runner’s speed running down is 50% less than r , mathematically:

  $\begin{array}{c}r-50\%\times r=r-\frac{50}{100}\times r\\ =r-\frac{r}{2}\\ =\frac{r}{2}\end{array}$

Thus, running down speed $\frac{r}{2}$

Now, expressions for time taken can be written as

  $\begin{array}{c}\text{Total time}=\left(\begin{array}{l}\text{time taken}\\ \text{running up}\end{array}\right)+\left(\begin{array}{l}\text{time taken}\\ \text{running down}\end{array}\right)\\ =\frac{\text{distance}}{\text{Speed running up}}+\frac{\text{distance}}{\text{Speed running down}}\\ =\frac{2}{r}+\frac{2}{\frac{r}{2}}\\ =\frac{2}{r}+\frac{2\times 2}{r}\\ =\frac{2}{r}+\frac{4}{r}\end{array}$

Thus expressions representing time taken is

  $\frac{2}{r}+\frac{4}{r}$