Chapter 1.9, Problem 10P

To determine

To calculate:

The number of miles of walkathon:

Answer to Problem 10P

The walking distance is $5\min$ , jogging distance is $10\min$ , hence $15\min$ is the walkathon.

Explanation of Solution

Given information:

Elisa walked certain distance at $5$ min/hr and then jogged twice that the distance at $8$ min/hr.

Total time of walking and jogging: $2$ hr and $15$ min

Calculation:

Let,

  $3x$ : Miles in the walkathon

  $2x$ : jogging distance

  $x$ : walking distance

Then convert $2$ hr and $15$ min to $2.25$ hrs

The equation of time:

  $T=\frac{D}{S}$

Where,

  $T$ : Time

  $D$ : Distance

  $S$ : Speed

  $\frac{x}{5}+\frac{2x}{8}=2.25\text{hrs}$

Multiply by $40$ :

  $\begin{array}{l}8x+5\left(2x\right)=40\left(2.25\right)\\ 8x+10x=90\\ 18x=90\\ x=\frac{90}{18}\\ x=5\min \end{array}$

  $x=5\min$ Walking, $10\min$ jogging, hence $15\min$ is the walkathon

Check the solution:

  $\begin{array}{l}\frac{5}{5}+\frac{10}{8}\\ 1+1.25=2.25\end{array}$

The walking distance is $5\min$ , jogging distance is $10\min$ , hence $15\min$ is the walkathon.