Question

Two trains, A and B, start from stations X and Y, 300 km apart, and travel towards each other. Train A travels at 60 km/h, and Train B travels at 90 km/h. If Train A starts 1 hour earlier than Train B, how long will it take for the two trains to meet after Train B starts?

Hint:

Remember: For objects moving towards each other, use relative speed (sum of speeds). Account for head starts by adjusting the initial distance before applying the time formula.

Answer 1

To solve the problem, we need to determine the time it takes for two trains traveling towards each other to meet, given different start times and speeds.

1. Understanding the Situation: 
- Distance between stations X and Y = 300 km 
- Speed of Train A = 60 km/h 
- Speed of Train B = 90 km/h 
- Train A starts 1 hour earlier than Train B 
- Let the time taken by Train B after it starts until the trains meet be t hours 
- In this time, Train A would have traveled for t + 1 hours

Key Concept: When two objects move towards each other, the distance covered together is the sum of the distances they travel individually. So, Distance = Distance by Train A + Distance by Train B

2. Setting Up the Equation: 
Let the meeting point be reached after t hours from the time Train B starts. 
Then: Distance covered by Train A = 60 × (t + 1) Distance covered by Train B = 90 × t 
According to the problem: $ 60(t + 1) + 90t = 300 $

3. Solving the Equation: 
Expanding the left side: $ 60t + 60 + 90t = 300 $ 
Combining like terms: $ 150t + 60 = 300 $ 
Subtract 60 from both sides: $ 150t = 240 $ 
Divide both sides by 150: $ t = \frac{240}{150} = 1.6 \, \text{hours} $

4. Converting to Minutes: 
$ 0.6 \, \text{hours} = 0.6 \times 60 = 36 \, \text{minutes} $ 
So, the time taken after Train B starts = 1 hour and 36 minutes

Final Answer: 
The two trains will meet 1 hour and 36 minutes after Train B starts.