Chapter 5.8, Problem 10P

To determine

To find the distance in kilometer when she did travel in all when total jogging time was $1h20\text{mins}$

Answer to Problem 10P

The total distance travelled was $10Km$

Explanation of Solution

Formula:

Given that Pam jogged up a hill at $6Km/hr$

and jogged back down at $10Km/hr$

total time for total jogging was $1h20\text{mins}\text{=}\frac{80}{60}=\frac{4}{3}hr$

Formula:

  $\text{speed=}\frac{\text{distance}}{\text{time}}$

Let total time be x

First, to determine the distance of the upward hill direction have speed $6km/hr$ in x hour

  $\text{Up}\text{Distance}=speed\times time=6\times x=6x(km)\mathrm{...............}(i)$

Now, determine the distance of the downward hill direction have speed $10km/hr$ in total $\left(\frac{4}{3}-x\right)$ hours.

  $\text{Down}\text{Distance}=speed\times time=10\times \left(\frac{4}{3}-x\right)\mathrm{...............}(ii)$

Thus , the distance travelled in down direction will be equal to up direction of hill.

Now, compare equation ( i ) and equation ( ii )

  $\begin{array}{c}6x=10\left(\frac{4}{3}-x\right)\\ 6x=\frac{40}{3}-10x\\ 6x+10x=\frac{40}{3}\\ 16x=\frac{40}{3}\\ x=\frac{40}{3\times 16}\\ =0.83hr\end{array}$

Now, $6x=6\times 0.83=5km$ is the distance up the hill which is equal to down to hill.

Hence,

  $\text{total}\text{distnace both the side =2}\times 5\text{=10 }\text{km}$