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

The walking rate = 1 mile per hour

The jogging rate = 3 miles per hour

Step-by-step explanation:

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

Let the rate at which you walked 3 miles = w

`\begin{gathered} w=(3)/(t) \\ \implies tw=3 \\ \implies t=(3)/(w) \end{gathered}`

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

Thus, jogging speed = 3w

`\begin{gathered} 3w=(3)/(T) \\ \implies3wT=3 \\ T=(3)/(3w) \\ T=(1)/(w) \end{gathered}`

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

`\begin{gathered} t+T=4 \\ (3)/(w)+(1)/(w)=4 \\ (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