A train running at a uniform speed of $72\text{ km/h}$ crosses an agricultural grain loading platform of length $250\text{ m}$ in $26\text{ seconds}$. What is the length of the train in meters?
Options:
(A) $270\text{ m}$
(B) $250\text{ m}$
(C) $220\text{ m}$
(D) $200\text{ m}$
Answer Key:
A
Step-by-Step Solution & Explanation
**Method 1: Standard Distance-Speed Formulation**
First convert speed from $\text{km/h}$ to $\text{m/s}$:
$v = 72 \times \frac{5}{18} = 20\text{ m/s}$
Total distance traveled while crossing the platform $= \text{Length of train } (L) + \text{Length of platform } (P)$:
$L + P = v \times t = 20\text{ m/s} \times 26\text{ s} = 520\text{ m}$
Given $P = 250\text{ m}$:
$L = 520 - 250 = 270\text{ m}$
Option **A** is correct.