Final answer:
The speeds of the passenger and freight trains are found by setting up equations using the formula d = rt and the information that the passenger train travels 20 mph faster than the freight train. Solving the resulting equation, we find that the passenger train's speed is 50 mph, and the freight train's speed is 30 mph.
Step-by-step explanation:
The question is asking to determine the speeds of both the passenger train and the freight train given that the passenger train overtakes the freight train three hours after it leaves and that it had departed 2 hours after the freight train. To solve this problem, we can use the information that distance is equal to rate multiplied by time (d = rt).
Let's denote the speed of the passenger train as v mph (miles per hour) and the freight train's speed as v - 20 mph, because the freight train travels 20 mph slower than the passenger train.
When the passenger train overtakes the freight train, both trains have traveled the same distance. By that time, the freight train has been traveling for 5 hours (since it left 2 hours earlier) and the passenger train for 3 hours.
The equation for the distance traveled by the passenger train is 3v, while for the freight train it's 5(v - 20). Since these distances are equal:
- 3v = 5(v - 20)
- 3v = 5v - 100
- 100 = 2v
- v = 50
So, the speed of the passenger train is 50 mph and the freight train's speed is 30 mph (50 - 20).
Therefore, the correct answer is C. Passenger train: 50 mph, Freight train: 30 mph.