Question

A train \( T_{1} \) runs at a speed of 50 kmph and \( T_{2} \) runs at a speed of 70 kmph. \( T_{1} \) starts at 8 am from a station and \( T_{2} \) starts from the same station in the same direction at 10 am. At what time do they meet?

• A. 5 pm
• B. 3 pm
• C. 4 pm
• D. 2 pm

Hint:

In relative speed problems for trains moving in the same direction, subtract the speeds. Always calculate the gap (head start) distance before applying the relative speed.

Answer 1

The Correct Option is B

Concept: This is a relative speed problem. Since the trains are moving in the same direction, the relative speed is the difference between their speeds. The catch-up time depends on the distance lead created by the first train.

Step 1: Calculate the distance covered by \( T_{1} \) before \( T_{2} \) starts.
\( T_{1} \) starts at 8 am, and \( T_{2} \) starts at 10 am. The head start time is 2 hours. \[ \text{Distance} = \text{Speed} \times \text{Time} = 50 \text{ kmph} \times 2 \text{ hours} = 100 \text{ km} \]

Step 2: Calculate the relative speed of the trains.
Since both trains are in the same direction: \[ \text{Relative Speed} = 70 \text{ kmph} - 50 \text{ kmph} = 20 \text{ kmph} \]

Step 3: Calculate the time taken for \( T_{2} \) to catch up with \( T_{1} \).
\[ \text{Time} = \frac{\text{Distance head start}}{\text{Relative Speed}} = \frac{100 \text{ km}}{20 \text{ kmph}} = 5 \text{ hours} \]

Step 4: Determine the meeting time.
\( T_{2} \) started at 10 am. It will meet \( T_{1} \) 5 hours after 10 am. \[ 10 \text{ am} + 5 \text{ hours} = 3 \text{ pm} \] \centerline{{3 pm}}