Question

A jogger runs from her home to a point A, which is 6 km away. For there 6 km, shebegins by running at a constant speed till she reaches a hilly portion 2 km from herhome. Here her speed slows down while she runs up the hill, which is a 1-km run.Then she speeds up while running down the hill.The last 2 km of the run are again atconstant speed. Draw a graph to show the jogger’s speed as a function of the distancefrom her home. Also find the range of this function.

Answer 1

Answer to Question #74724, Math / Calculus

A jogger runs from her home to a point A, which is $6 \, \text{km}$ away. For there $6 \, \text{km}$ , she begins by running at a constant speed till she reaches a hilly portion $2 \, \text{km}$ from her home. Here her speed slows down while she runs up the hill, which is a $1 \, \text{km}$ run. Then she speeds up while running down the hill. The last $2 \, \text{km}$ of the run are again at constant speed. Draw a graph to show the jogger's speed as a function of the distance from her home. Also find the range of this function.

Solution.

Let $V_{1}$ is jogger speed at the distance from home to the hill, $V_{2}$ is jogger speed at the distance from the hill to the point A, $V_{\min}$ is jogger speed at the peak of the hill.

Then we have two cases.

The first case $V_{1} > V_{2}$ :

The second case $V_{1} < V_{2}$ :

The range of $V(s):V_{min}\leq V(s)\leq \max (V_1,V_2)$

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