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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.

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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.

Two trains leave stations 588 miles apart at the same time and travel toward each other. One train travels at 115 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet?

Solve the problem where two trains leave stations 588 miles apart and travel toward each other at speeds of 115 mph and 95 mph. This step-by-step solution explains how to calculate the time it takes for the two trains to meet using the concept of relative speed. Suitable for Grades 8-10.

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