Two tourists went on a hike at dawn. One went from a to b and another one went from b to a. They met at noon but did not stop and continued walking maintaining same speed for the whole trip. One finished his hike at 4pm in B and another one came to A at 9 pm. At what hour was dawn that day?
To determine the hour of dawn on that day, we need to analyze the information given. Let's break down the steps to solve the problem:
1. Identify the time it took each tourist to complete their hike:
- The tourist who traveled from A to B finished at 4 pm, which means this hike lasted 8 hours.
- The tourist who traveled from B to A arrived at A at 9 pm, meaning this hike lasted 9 hours.
2. Determine the total time the tourists spent hiking:
- Since they met at noon and continued walking without stopping, the hiking time for both tourists combined is 12 hours. Therefore, we can conclude that the total hiking time is 12 hours.
3. Calculate the time of dawn:
- The difference in hiking times between the two tourists is 1 hour (9 hours - 8 hours).
- Since they traveled at the same speed for the entire trip, their meeting point at noon should be halfway between A and B.
- As they hiked for a total of 12 hours, each tourist would have spent 6 hours on their journey until noon.
- Since they began their hikes at dawn, we need to subtract the 6 hours they spent hiking before noon to determine the hour of dawn.
- Subtracting 6 hours from 9 pm (the time the tourist from B arrived at A) yields 3 am.
Therefore, the hour of dawn on that day was 3 am.