Discussion
A train overtakes two boys who are running at the rate of 8 km/hr and 16 km/hr in the same direction as the train. The train completely passes them in 36 seconds and 40 seconds respectively. What is the length of the train?
Answer: C
Let the train's speed be \( v \) km/hr. Passing each boy covers the train's own length at the relative speed.
\[ L = (v - 8) \times \frac{5}{18} \times 36 = (v - 16) \times \frac{5}{18} \times 40 \]
The factor \( \tfrac{5}{18} \) is common:
\[ 36(v - 8) = 40(v - 16) \quad\Longrightarrow\quad 36v - 288 = 40v - 640 \]
\[ 4v = 352 \quad\Longrightarrow\quad v = 88 \text{ km/hr} \]
\[ L = (88 - 8) \times \frac{5}{18} \times 36 = 80 \times 10 = 800 \text{ m} \]
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