Chapter 6.1, Problem 42PPE

a.

To determine

To calculate:System of equation that models the situation.

Answer to Problem 42PPE

  $\begin{array}{l}y=6+4x\\ y=1+3x\end{array}$

Explanation of Solution

Calculation:

Let’s say $y$ is the distance covered by the hikers and $x$ is the time travelled.

Now, the first hiker starts at point $6$ mi from the beginning of the trail and walks at a speed of $4$ mi/h

  $\therefore y=6+4x$

Now, the second hiker starts $1$ mi from the beginning and walks at a speed of $3$ mi/h

  $\therefore y=1+3x$

b.

To determine

To calculate: Graph the equations and determine the intersection point.

Answer to Problem 42PPE

  $(-5,-14)$

Explanation of Solution

Calculation:

  

From the graph, intersection point is, $(-5,-14)$

c.

To determine

To calculate:Is the intersection point meaningful in this situation? Explain.

Answer to Problem 42PPE

No

Explanation of Solution

Calculation:

Here, intersection point is in third quadrant. That means for a negative time and distance two hikers are meeting. Negative time is never possible. Therefore, the hikers will never meet. Intersection point does not have any meaning in this situation.