To determine how long it will take for the two trains to meet, we can use the following steps:

Step 1: Calculate the relative speed

Since the trains are moving toward each other, their relative speed is the sum of their individual speeds.

$\text{Relative speed} = 105 \text{ miles per hour} + 85 \text{ miles per hour} = 190 \text{ miles per hour}$

Step 2: Use the formula for time

The time it takes for the two trains to meet can be found using the formula:

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Here, the distance between the two stations is 304 miles, and the relative speed is 190 miles per hour.

$\text{Time} = \frac{304 \text{ miles}}{190 \text{ miles per hour}} \approx 1.6 \text{ hours}$

Step 3: Convert time to hours and minutes

To convert 1.6 hours into hours and minutes:

$1.6 \text{ hours} = 1 \text{ hour and } 0.6 \times 60 \text{ minutes} = 1 \text{ hour and } 36 \text{ minutes}$

Final Answer

The two trains will meet in approximately 1 hour and 36 minutes.

Would you like more details, or do you have any questions?

Here are five related questions:

1. What if the trains started 500 miles apart with the same speeds?
2. How would the meeting time change if one train's speed decreased by 20 miles per hour?
3. What is the distance each train travels before they meet?
4. How long would it take if both trains traveled at 95 miles per hour?
5. What would be the meeting time if one train started 1 hour later?

Tip: Always check if both objects are moving toward each other or in the same direction when calculating relative speed.