Final answer:
By calculating the head start of the first train and using the relative speeds of both trains, it turns out that the second train will overtake the first train at 8 PM, which is not one of the provided choices.
Step-by-step explanation:
The question involves solving for the time at which the second train overtakes the first by using the concepts of speed, distance, and time. First, we need to calculate how far the first train travels by 10 AM, which is the time the second train starts. The first train travels for 2 hours at 45 mph, giving it a head start of 90 miles. Then we'll use the relative speed between the two trains to determine how long it takes for the second train to cover this distance. The second train's speed relative to the first is the difference between their speeds, which is 54 mph - 45 mph = 9 mph.
Next, we divide the head start distance by the relative speed to find the time it takes for the second train to catch up: 90 miles ÷ 9 mph = 10 hours. Adding this time to the 10 AM departure of the second train, we get an overtaking time of 8 PM. Therefore, none of the answer choices provided (a) 1:30 PM, (b) 2:30 PM, (c) 3:00 PM, or (d) 3:30 PM are correct.