Question

Two trains of length 150 m each pass each other in 20 s when moving in opposite directions. When they move in the same direction, they take 40 s to pass each other completely. Find the speed of the faster train.

• A. 10.25 m/sec
• B. 11.25 m/sec
• C. 11.75 m/sec
• D. 12 m/sec

Hint:

When solving train problems, always use the total distance covered = sum of lengths, and apply relative speed formulas. Opposite direction means add speeds, same direction means subtract speeds.

Answer 1

The Correct Option is B

Step 1: Relative speed when moving in opposite directions.
Each train length = 150 m. Distance to cross completely = \(150+150=300\) m. \[ v_1+v_2=\frac{\text{distance}}{\text{time}}=\frac{300}{20}=15\ \text{m/s} \quad (1) \] Step 2: Relative speed when moving in the same direction.
\[ v_1-v_2=\frac{300}{40}=7.5\ \text{m/s} \quad (2) \] Step 3: Solve equations (1) and (2).
Add: \((v_1+v_2)+(v_1-v_2)=15+7.5\) \[ 2v_1=22.5 \quad \Rightarrow \quad v_1=11.25\ \text{m/s} \] Substitute back: \(v_2=15-11.25=3.75\ \text{m/s}\). \[ \boxed{\text{Speed of the faster train} = 11.25\ \text{m/s}} \]