A freight train left a station at 12 noon, going north at a rate of 50 miles per hour. At 1:00 P.M. a passenger train left the same station, going south at a rate of 60 miles per hour. At what time were the trains 380 miles apart?

Options

A. 3:00 P.M.
B. 4:00 P.M.
C. 4:30 P.M.
D. 5:00 P.M.

Answer

To solve the problem of when the freight train and the passenger train are 380 miles apart, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Departure Times and Speeds**:
- The freight train leaves at 12:00 PM traveling north at 50 miles per hour.
- The passenger train leaves at 1:00 PM traveling south at 60 miles per hour.

2. **Calculate the Distance Traveled by the Freight Train by 1:00 PM**:
- From 12:00 PM to 1:00 PM, the freight train travels for 1 hour.
- Distance = Speed × Time = 50 miles/hour × 1 hour = 50 miles.
- At 1:00 PM, the freight train is 50 miles north of the station.

3. **Determine the Remaining Distance to Reach 380 Miles Apart**:
- The total distance we want between the two trains is 380 miles.
- At 1:00 PM, the distance between the two trains is 50 miles.
- Remaining distance = 380 miles - 50 miles = 330 miles.

4. **Calculate the Relative Speed of the Two Trains**:
- After 1:00 PM, both trains are moving away from each other.
- The relative speed = Speed of freight train + Speed of passenger train = 50 miles/hour + 60 miles/hour = 110 miles/hour.

5. **Calculate the Time Required to Cover the Remaining Distance**:
- Time = Distance / Speed = 330 miles / 110 miles/hour = 3 hours.

6. **Determine the Final Time**:
- Since the passenger train starts moving at 1:00 PM, we add the 3 hours to this time.
- 1:00 PM + 3 hours = 4:00 PM.

### Conclusion:
The trains will be 380 miles apart at **4:00 PM**.

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