Discussion
A walks from points Jammu to Delhi and at the same time B starts walking from Delhi to Jammu. After passing each other, they complete their journeys in 361 hours and 289 hours, respectively. Find the ratio of speed of A to that of B?
Answer: A
Two travellers who start together and meet, then finish in times \( t_{A} \) and \( t_{B} \), have speeds in the ratio
\[ \frac{v_{A}}{v_{B}} = \sqrt{\frac{t_{B}}{t_{A}}} \]
\[ \frac{v_{A}}{v_{B}} = \sqrt{\frac{289}{361}} = \frac{17}{19} \]
The square root is the part most often missed: taking the times' ratio directly would give 289 : 361, which is offered as a distractor. It is a square root because each traveller's remaining distance is the distance the other has already covered.
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