A hiker started to climb up the hill at 6:00 am and either kept climbing up or rested at some place(s). He reached the top at 6:00 pm. he rested there for the next 12 hours. Next day at 6:00 am, he began to travel down the same path. He either moved downward or rested at some place(s). For the up and down trips, how many times was he at the same place at the same time?
Once -- at the halfway mark. That's assuming he took 12 hours to go down.
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once
To determine the number of times the hiker was at the same place at the same time during both the upward and downward trips, we need to consider the time intervals and durations involved.
Let's analyze the problem step by step:
1. The hiker starts climbing up the hill at 6:00 am and reaches the top at 6:00 pm. This means the upward journey took 12 hours.
2. The hiker then rests at the top for the next 12 hours, from 6:00 pm until 6:00 am the next day.
3. At 6:00 am the following day, the hiker begins to travel down the same path.
4. We need to determine the number of times he was at the same place during both the upward and downward trips.
Based on the given information, we can identify a few instances where the hiker was at the same place at the same time:
1. When the hiker started climbing up at 6:00 am, he was at the same place as when he began descending at 6:00 am the next day.
2. When the hiker reached the top at 6:00 pm, he was at the same place as when he started descending at 6:00 am the next day.
3. If the hiker rested along the path during both trips, there might be additional instances of being at the same place at the same time.
Without additional information about rest durations or locations during the trips, it is challenging to determine the exact number of times the hiker was at the same place at the same time. However, we do know there are at least two instances:
1. At the start of the hiker's descent (6:00 am on the second day), he is at the same place as when he started climbing up (6:00 am on the first day).
2. At the end of the hiker's descent (the moment he reaches the starting point), he is at the same place as when he reached the top of the hill on the first day.