Let \(x\) km represent the distance each individual traveled from their starting point to the meeting location.
Arvind's speed is 54 km/h. The distance he covers after meeting Surbhi is:
\[ \text{Distance}_{\text{remaining\_Arvind}} = 54 \text{ km/h} \times 6 \text{ h} = 324 \text{ km} \]
This indicates:
\[ x = \text{Total Distance} - 324 \]
Surbhi takes 24 hours to cover her remaining distance after meeting Arvind. Let Surbhi's speed be \(v\) km/h. The distance she travels after meeting Arvind is:
\[ \text{Distance}_{\text{remaining\_Surbhi}} = v \text{ km/h} \times 24 \text{ h} \]
Since they meet at the same point, the sum of their distances traveled to that point equals the total distance:
\[ x + v \times 24 \text{ h} = \text{Total Distance} \]
Given that they traveled for equal durations until meeting, Surbhi's travel time for her remaining journey is four times Arvind's:
\[ \frac{v}{54} = \frac{1}{4} \]
Therefore, Surbhi's speed is calculated as:
\[ v = \frac{54}{4} = 13.5 \text{ km/h} \]
Using Surbhi's speed to determine her remaining distance:
\[ \text{Distance}_{\text{remaining\_Surbhi}} = 13.5 \text{ km/h} \times 24 \text{ h} = 324 \text{ km} \]
The total distance is thus:
\[ \text{Total Distance} = 324 \text{ km} + 324 \text{ km} = 972 \text{ km} \]
The distance between town A and town B is 972 km.