The question asks how long it will take for two trains to meet if they are 442 miles apart, with one train traveling at 90 miles per hour and the other at 80 miles per hour.

Solution:

The total distance between the two trains is 442 miles. The two trains are traveling toward each other, so their speeds add up.

Combined Speed:

$\text{Combined speed} = 90 + 80 = 170 \, \text{miles per hour}.$

Time to Meet:

The time for the two trains to meet is given by the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Substitute the values: $\text{Time} = \frac{442}{170} \approx 2.6 \, \text{hours}.$

Final Answer:

$\boxed{2.6 \, \text{hours}}$

Would you like a detailed explanation of how this applies to similar problems or further clarification?

Related Questions:

1. What would happen if the two trains started at different times?
2. How does the solution change if one train stops after traveling a certain distance?
3. What is the relative speed of one train from the perspective of the other?
4. How can this problem be solved graphically?
5. Can this problem be adapted to three or more objects moving towards each other?

Tip:

When solving problems involving relative motion, always consider whether the objects are moving towards or away from each other to decide if speeds are added or subtracted.