The train would arrive in city B at around 6:59 PM.
Let's break down the problem step by step:
1. The train leaves city A at 12:00 and travels at an average speed of 60 mph towards city B, which is 200 miles away. To cover this distance, it would take the train 200 miles / 60 mph = 3.33 hours.
2. However, along the way, the train breaks down at the top of a hill and rolls backwards for 1 mile at a constant pace of 3 mph. This backward motion takes the train 1 mile / 3 mph = 0.33 hours.
3. After reaching the bottom of the hill, the train resumes its travel to city B, again averaging 60 mph. Since the remaining distance to city B is now 199 miles (200 miles - 1 mile), it would take the train 199 miles / 60 mph = 3.32 hours to cover this distance.
4. To find out what time the train arrives in city B, we need to add up the times from steps 1, 2, and 3.
- The time it takes the train to travel from city A to the top of the hill is 3.33 hours.
- The time it takes the train to roll backward for 1 mile is 0.33 hours.
- The time it takes the train to travel from the bottom of the hill to city B is 3.32 hours.
Therefore, the total time is 3.33 hours + 0.33 hours + 3.32 hours = 6.98 hours.
5. Adding this total time of 6.98 hours to the departure time of 12:00, we can calculate the arrival time in city B.
12:00 + 6.98 hours = 6:59 PM (approximately).
The train would arrive in city B at around 6:59 PM.