Linear Graphs in Real Life Problems

Hiker I starts climbing the mountain at \(0000\)h. At the same time, Hiker II starts descending from the mountain top. A supply station is located somewhere between the top and the foot of the mountain, where both hikers stop by to take a rest. The height-time graph below shows the heights of the two hikers after \(0000\)h.

1. Find, in metres, the height of the mountain, and the height of the supply station from the foot of the mountain.
2. Find the duration of time in minutes
   1. for Hiker I to climb to \(400\)m in height,
   2. for Hiker II to descend to \(400\)m in height,
   3. Hiker I and II spend at the supply station, respectively.
3. Find the gradient of each of the following line segments, and state clearly what each gradient represents.
   1. \(OA\),
   2. \(AF\),
   3. \(CD\),
   4. \(DK\).
4. Which hiker arrives at the supply station earlier? Explain your answer.
5. From the graph, will the two hikers meet each other on their journey? If yes, approximately state the time when they meet each other. If no, state your reason. Assume that there is only one road on the mountain.
6. Find the duration of time when the difference of height between the two hikers is less than or equal to \(200\)m.