To solve the problem where two trains are traveling towards each other, we need to use the concept of relative speed.

Given:

• Distance between stations = 588 miles
• Speed of the first train = 115 miles per hour
• Speed of the second train = 95 miles per hour

Step-by-step solution:

1. Total relative speed: Since both trains are moving towards each other, their speeds add up. $115 \, \text{mph} + 95 \, \text{mph} = 210 \, \text{mph}$

2. Time to meet: To find the time it takes for the trains to meet, we divide the total distance by the relative speed. $\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{588 \, \text{miles}}{210 \, \text{mph}} = 2.8 \, \text{hours}$

Thus, it will take 2.8 hours for the two trains to meet.

Would you like further details on this solution? Here are some related questions for deeper understanding:

1. How do you calculate the relative speed of objects moving toward each other?
2. What if one of the trains started later than the other? How would that affect the time calculation?
3. If the distance was different, say 700 miles, how would that affect the solution?
4. How would the problem change if the trains were moving away from each other?
5. What role does speed play in distance-time calculations?

Tip: Always remember, when two objects move towards each other, their relative speed is the sum of their individual speeds.