Question

A train crosses a man walking in the same direction as that of the train at the speed of 26 m/s in 13 seconds and a boy walking in the opposite direction of that of the train at the speed of 18 m/s in 11 seconds. What is the speed of the train?

• A. 67 m/s
• B. 134 m/s
• C. 268 m/s
• D. 536 m/s

Answer 1

The Correct Option is C

Step 1: Define Variables 

• Let the speed of the train be v m/s.
• Let the length of the train be L meters.

Step 2: Formulating Equations

When the train crosses a man walking in the same direction, the relative speed is \( v - 26 \). The time taken is 13 seconds, so:

\( L = (v - 26) \times 13 \).

When the train crosses a boy walking in the opposite direction, the relative speed is \( v + 18 \). The time taken is 11 seconds, so:

\( L = (v + 18) \times 11 \).

Step 3: Equating Both Expressions for L

\[ (v - 26) \times 13 = (v + 18) \times 11 \]

Step 4: Simplifying

Expanding both sides:

\[ 13v - 338 = 11v + 198 \]

Rearranging:

\[ 2v = 536 \]

Solving for \( v \):

\[ v = 268 \]

Conclusion

The speed of the train is 268 m/s.