Final answer:
The minimum headway for opposite-direction train travel in a single-track tunnel with a one-way travel time of 4½ minutes is approximately 4½ minutes to account for both directions and safety intervals. Calculation of average speed involves total distance and total travel time.
Step-by-step explanation:
The minimum headway in one direction for trains running in opposite directions on a single track can be calculated if we know the running time for the train to pass through the tunnel is 4½ minutes in one direction.
Assuming trains need to clear the tunnel before another can enter, the first train takes 4½ minutes to exit the tunnel, and we must then allow for the same amount of time for a train coming in the opposite direction, equaling a total of 9 minutes. Therefore, the minimum headway in one direction would be slightly less than half of that time, due to the need for safety intervals and coordination, so it would be approximately 4½ minutes for safe operation.
Additionally, to calculate average speed as related in the supplementary information, we must note that the total distance traveled by the train is 80 miles (40 miles each way). The total time taken is 1 hour and 45 minutes, or 105 minutes. Therefore, the average speed of the train in mph is found by dividing the total distance by the total time taken to travel that distance.