Question

As part of an exercise regimen, you walk 3 miles on an indoor track. Then you jog atthree times your walking speed for another 3 miles. If the total time spent walking andjogging is 4 hours, find the walking and jogging rates.

Answer 1

Answer:

The walking rate = 1 mile per hour

The jogging rate = 3 miles per hour

Explanation:

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

Let the rate at which you walked 3 miles = w

$\begin{gathered} w=\frac{3}{t} \\ \implies tw=3 \\ \implies t=\frac{3}{w} \end{gathered}$

You jog three times your walking speed for another 3 miles.

Thus, jogging speed = 3w

$\begin{gathered} 3w=\frac{3}{T} \\ \implies3wT=3 \\ T=\frac{3}{3w} \\ T=\frac{1}{w} \end{gathered}$

If the total time spent walking and jogging is 4 hours, then we have:

$\begin{gathered} t+T=4 \\ \frac{3}{w}+\frac{1}{w}=4 \\ \frac{3+1}{w}=4 \\ 4w=4 \\ w=1\text{ mile per hour} \end{gathered}$

Thus:

• The walking rate, w = 1 mile per hour

,

• The jogging rate. 3w = 3 miles per hour