Final answer:
The speed of the first train is 20 mph and that of the second train, which travels 60 mph faster, is 80 mph. We find these speeds by equating the distances each train covers until the second one overtakes the first and solving for the unknown speed.
Step-by-step explanation:
To solve the problem of the two trains leaving New York, we need to use the concepts of distance, speed, and time. We know the second train travels 60mph faster than the first and overtakes it in 2 hours. Let's denote the speed of the first train as s mph. Therefore, the speed of the second train is s + 60 mph.
We can calculate the distances covered by both trains during the time interval when the second train is traveling, which is from 6:00 pm to 8:00 pm, a total of 2 hours.
Distance covered by the first train: D1 = s * 4 hours (since it started at 4:00 pm and was overtaken at 8:00 pm).
Distance covered by the second train: D2 = (s + 60) * 2 hours.
Since the second train catches up with the first, D1 must equal D2. By setting up the equation s * 4 = (s + 60) * 2, we can solve for s.
- 8s = 2s + 120
- 6s = 120
- s = 20 mph
This means the speed of the first train is 20 mph and the speed of the second train is 80 mph (20 mph + 60 mph).