A train left Hanson's town and traveled for 4 hours and 20 minutes to Vindale. Then it traveled 3 hours and 20 minutes and arrived in Somerville at 8:20 P.M. What time did the train leave Hanson's town?

To determine the time the train left Hanson's town, we need to calculate the total time traveled and subtract it from the arrival time in Somerville.

### Steps:
1. **Convert the travel times to minutes**:
   - 4 hours and 20 minutes = \( 4 \times 60 + 20 = 260 \) minutes.
   - 3 hours and 20 minutes = \( 3 \times 60 + 20 = 200 \) minutes.
   - Total travel time = \( 260 + 200 = 460 \) minutes.

2. **Arrival time at Somerville**: 8:20 P.M.

3. **Subtract the total travel time from the arrival time**:
   - Convert 8:20 P.M. to 24-hour format: 8:20 P.M. = 20:20.
   - Subtract the total travel time (460 minutes) from 20:20:
     - \( 460 \) minutes is equivalent to \( 7 \) hours and \( 40 \) minutes.
     - Subtract 7 hours and 40 minutes from 20:20:
     - \( 20:20 - 7:40 = 12:40 \).

Thus, the train left Hanson's town at **12:40 P.M.** (noon).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the calculation change if the train had a 30-minute layover in Vindale?
2. What if the train traveled 20% faster from Hanson's town to Vindale?
3. How would the departure time change if the train reached Somerville at 9:30 P.M. instead?
4. Can we calculate the average speed if the total distance between Hanson's town and Somerville is 300 miles?
5. If the train left Vindale at 2:00 P.M., when did it arrive at Somerville?

**Tip**: When solving time-related problems, converting all times into minutes first often simplifies calculations.

Learn how to calculate the departure time of a train that traveled for a total of 7 hours and 40 minutes and arrived at Somerville at 8:20 P.M. This time-related problem involves converting hours and minutes and subtracting them from the arrival time to find the departure time.

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