To solve this problem, let’s analyze the information given step-by-step:

Step 1: Determine the Time Difference between Cities

The question states that:

• When it is 6:00 AM on June 1st in Ben's city, it is 10:30 PM on May 31st in Amy's city.

Calculating the time difference:

• From 10:30 PM on May 31st in Amy’s city to 6:00 AM on June 1st in Ben's city, there is a difference of 7.5 hours (6 hours from 10:30 PM to 4:30 AM, and then 1.5 more hours to reach 6:00 AM).
• Therefore, Amy’s city is 7.5 hours behind Ben’s city.

Step 2: Departure and Arrival Times in Ben's Time Zone

The train departs from Amy's city at 11:20 PM on June 1st (Amy's local time). We need to convert this to Ben’s time zone by adding 7.5 hours:

• $11:20 \, \text{PM} + 7.5 \, \text{hours} = 6:50 \, \text{AM on June 2nd}$ in Ben’s city.

The train arrives in Ben's city at 9:05 AM on June 2nd (Ben’s local time).

Step 3: Calculate the Duration of the Journey

Now, we have the departure and arrival times in Ben's time zone:

• Departure: 6:50 AM on June 2nd
• Arrival: 9:05 AM on June 2nd

To find the journey time:

• From 6:50 AM to 9:05 AM is 2 hours and 15 minutes (or 2.25 hours).

Step 4: Calculate the Average Speed

The distance covered during the journey is 850 kilometers.

Using the formula for average speed: $\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}$ Substitute the values: $\text{Average Speed} = \frac{850 \text{ km}}{2.25 \text{ hours}} \approx 378 \text{ km/h}$

Answer

The average speed of the train is approximately 378 km/h.

Would you like further explanation on any of the steps, or have any specific questions?

Here are some related questions that might deepen your understanding:

1. How would the solution change if the cities had a different time difference?
2. Can you explain why it's important to convert both times to the same time zone?
3. What would be the average speed if the distance was different but time remained the same?
4. How would rounding affect the final answer in problems like this?
5. Can you determine the time in Amy's city when the train arrives in Ben's city?

Tip: When dealing with time zone conversions, it’s often helpful to write down each time change step-by-step to avoid confusion.