Answer
a.)
$d=4t+6$
$d=3t+1$
b.) Refer to Image
c.) No. As the intersection point is $(-5,-14)$ it implies that the two lines intersect when in reality, the two hikers will never actually meet, as time cannot be negative ($-5<0$).
Work Step by Step
a.)
For Hiker 1: $s = 4mi/h$ and $d_{0} = 6mi$
This implies, $d=4t+6$
For Hiker 2: $s=3mi/h$ and $d_{0}=1mi$
This implies, $d=3t+1$
Therefore, the system of equations becomes,
$$d=4t+6$$
$$d=3t+1$$
NOTE: We are assuming that the distance from the beginning is a positive value since the trail is a "marked" one, implying that the hikers must be a positive distance from the start.
b.) Use any graphing method (hand-drawn or digital) to plot $y=4x+6$ and $y=3x+1$ to find the intersecting point (use $x$ and $y$ to avoid confusion). Refer to the image.
c.) The point of intersection for $d=4t+6$ and $d=3t+1$ is $(-5,-14)$ as seen in b.).
