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

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

Step 1: Calculate the relative speed

When two objects are moving towards each other, their relative speed is the sum of their individual speeds.

$\text{Relative Speed} = 80 \, \text{km/h} + 70 \, \text{km/h} = 150 \, \text{km/h}$

Step 2: Use the formula

The total distance between the two trains is 300 km. Using the formula:

$\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{300 \, \text{km}}{150 \, \text{km/h}} = 2 \, \text{hours}$

Final Answer:

The two trains will meet in 2 hours.

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Would you like to see a graphical explanation or further details? Here are some related questions to deepen your understanding:

1. What if the two trains had different starting distances?
2. How would the time change if one train's speed increased by 10 km/h?
3. What happens if the two trains were traveling away from each other instead?
4. How is the relative speed formula derived?
5. Can this problem be solved graphically or using calculus?

Tip: When dealing with relative motion, always consider the direction of the objects to determine whether to add or subtract their speeds.