Question

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is,

• A. 48 km/hr
• B. 54 km/hr
• C. 66 km/hr
• D. 82 km/hr

Hint:

Add both train lengths to get the crossing distance, divide by the time to get relative speed, then subtract the known train's speed since they move toward each other.

Answer 1

The Correct Option is D

This problem can also be worked entirely in metres per second first, converting only the final answer back to km/hr.

1. Convert Train A's speed to m/s: $50 \text{ km/hr} = 50 \times \frac{5}{18} = \frac{250}{18} = 13.89$ m/s.
2. The combined length to be covered while crossing is $108 + 112 = 220$ m, covered in $6$ s, so the relative speed is $\frac{220}{6} = 36.67$ m/s.
3. Since the trains move toward each other, relative speed equals the sum of individual speeds: $13.89 + v_B = 36.67$, where $v_B$ is Train B's speed in m/s.
4. Solve for $v_B$: $v_B = 36.67 - 13.89 = 22.78$ m/s.
5. Convert $v_B$ back to km/hr: $22.78 \times \frac{18}{5} = 82$ km/hr.

Working in m/s throughout gives the same speed for the second train as converting the relative speed to km/hr first.

\[\boxed{82 \text{ km/hr}}\]