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

The objective is to calculate the meeting time of two trains approaching each other, considering their staggered departure times and distinct velocities.

1. Fundamental Principles:

- Combined Velocity: For objects moving towards each other, their relative speed is the sum of their individual speeds.
- Temporal Offset: Any distance covered by an earlier-starting object during its head start period must be accounted for.
- Convergence Point: The location where the aggregate distance traveled by both objects equals the initial separation.

2. Provided Data:

Separation between stations = \( 300 \text{ km} \)
Velocity of Train A = \( 60 \text{ km/h} \)
Velocity of Train B = \( 90 \text{ km/h} \)
Train A departs \( 1 \text{ hour} \) prior to Train B.

3. Temporal Calculation:

Let \( t \) represent the duration (in hours) Train B travels until the meeting occurs.
Consequently, Train A will have traveled for \( t + 1 \) hours.

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

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

Concluding Result:

The two trains will intersect 1.6 hours (equivalent to 1 hour and 36 minutes) subsequent to Train B's departure.