The objective is to calculate the meeting time of two trains traveling towards each other, considering their distinct departure times and speeds.
1. Problem Setup:
- Distance between stations X and Y = 300 km
- Speed of Train A = 60 km/h
- Speed of Train B = 90 km/h
- Train A departs 1 hour before Train B
- Let t be the time in hours Train B travels until the trains meet
- Consequently, Train A travels for t + 1 hours
Core Principle: When two objects move towards each other, their combined distance covered equals the sum of their individual distances traveled. Thus, Total Distance = Distance covered by Train A + Distance covered by Train B
2. Equation Formulation:
Assuming the meeting occurs t hours after Train B's departure:
Distance covered by Train A = 60 × (t + 1) Distance covered by Train B = 90 × t
The problem equation is: $ 60(t + 1) + 90t = 300 $
3. Equation Solution:
Expanding the equation: $ 60t + 60 + 90t = 300 $
Combining terms: $ 150t + 60 = 300 $
Subtracting 60 from both sides: $ 150t = 240 $
Dividing by 150: $ t = \frac{240}{150} = 1.6 \, \text{hours} $
4. Time Conversion:
$ 0.6 \, \text{hours} = 0.6 \times 60 = 36 \, \text{minutes} $
Therefore, the time elapsed after Train B starts is 1 hour and 36 minutes.
Conclusion:
The two trains will intersect 1 hour and 36 minutes subsequent to Train B's departure.