Final answer:
The average speed of the train is 12.31 miles per hour. The trip to Washington DC takes approximately 26 minutes and 24 seconds, while the return trip takes approximately 40 minutes and 12 seconds.
Step-by-step explanation:
The average speed of the train can be calculated by dividing the total distance traveled by the total travel time. In this case, the train travels 40 miles one way and 40 miles back, for a total distance of 80 miles. The total travel time is given as 6.5 hours. So, the average speed of the train is 80 miles / 6.5 hours = 12.31 miles per hour.
To find the time taken for each trip, we can use the formula time = distance / speed. For the trip to Washington DC, the distance is 40 miles and the speed is 90 miles per hour. So, the time taken for this trip is 40 miles / 90 miles per hour = 0.44 hours, which is approximately 26 minutes and 24 seconds.
For the return trip, the distance is again 40 miles, but the speed is 60 miles per hour. So, the time taken for the return trip is 40 miles / 60 miles per hour = 0.67 hours, which is approximately 40 minutes and 12 seconds.