Discussion
Two trains A and B start from Jammu and Chennai towards Chennai and Jammu, respectively. From the moment they pass each other, they take 24 hrs 30 minutes and 18 hrs to reach Chennai and Jammu, respectively. The train from Jammu is running at 120 km/hr. What is the speed of the train starting from Chennai?
Answer: B
Two trains that meet and then take \( t_{A} \) and \( t_{B} \) to finish have speeds in the ratio
\[ \frac{v_{A}}{v_{B}} = \sqrt{\frac{t_{B}}{t_{A}}} \]
Here \( t_{A} = 24\tfrac{1}{2} \) h and \( t_{B} = 18 \) h:
\[ \frac{v_{A}}{v_{B}} = \sqrt{\frac{18}{24.5}} = \sqrt{\frac{36}{49}} = \frac{6}{7} \]
\[ v_{B} = 120 \times \frac{7}{6} = 140 \text{ km/hr} \]
The square root is essential: taking the times' ratio directly would give about 163 km/hr.
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