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?

• A. 1.5 hours
• B. 1.6 hours
• C. 2.5 hours
• D. 3 hours

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

The Correct Option is B

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

1. Understanding the Concepts:

- Relative Speed: When two objects move towards each other, their relative speed is the sum of their individual speeds.
- Time Difference: If one train starts earlier, the distance it covers during that time must be considered.
- Meeting Point: The point where the combined distances covered by both trains equals the total distance between them.

2. Given Values:

Distance between stations = \( 300 \text{ km} \)
Speed of Train A = \( 60 \text{ km/h} \)
Speed of Train B = \( 90 \text{ km/h} \)
Train A starts \( 1 \text{ hour} \) earlier than Train B

3. Calculating the Time:

Let \( t \) be the time (in hours) Train B travels before meeting Train A.
Then, Train A travels for \( t + 1 \) hours.

Distance covered by Train A = \( 60 \times (t + 1) \)
Distance covered by Train B = \( 90 \times t \)

Since the total distance is 300 km:
\[ 60(t + 1) + 90t = 300 \]
\[ 60t + 60 + 90t = 300 \]
\[ 150t + 60 = 300 \]
\[ 150t = 240 \Rightarrow t = \frac{240}{150} = 1.6 \text{ hours} \]

Final Answer:

The two trains will meet 1.6 hours (or 1 hour 36 minutes) after Train B starts.