Question

Two trains 130 m and 110 m long are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of each train?

• A. \(42\) m/s, \(38\) m/s
• B. \(36\) m/s, \(42\) m/s
• C. \(38\) m/s, \(36\) m/s
• D. \(40\) m/s, \(36\) m/s
• E. \(42\) m/s, \(36\) m/s

Answer 1

The Correct Option is A

Concept:

• Same direction: relative speed = difference
• Opposite direction: relative speed = sum

Step 1: Total length.
\[ 130 + 110 = 240 \text{ m} \]
Step 2: Opposite direction.
\[ \text{Relative speed} = \frac{240}{3} = 80 \text{ m/s} \] \[ v_1 + v_2 = 80 \quad \cdots (1) \]
Step 3: Same direction.
\[ \text{Relative speed} = \frac{240}{60} = 4 \text{ m/s} \] \[ v_1 - v_2 = 4 \quad \cdots (2) \]
Step 4: Solve equations.
\[ v_1 + v_2 = 80,\quad v_1 - v_2 = 4 \] \[ 2v_1 = 84 \Rightarrow v_1 = 42 \] \[ v_2 = 38 \]
Step 5: Option analysis.

• (A) Correct \checkmark
• Others incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).