The problem states that there are two buses, A and B, traveling between three stations S1, S2, and S3. Bus A starts its journey from S1, while Bus B starts its journey from S2. The distance between S1 and S2 is not given, but we are told that the distance between S1 and S3 is 60% of the distance between S1 and S2.


- Bus A starts at 11 am from S1 and travels towards S2.
- Bus B starts at 12 pm from S2 and travels towards S1.
- Bus B has a speed of 75% of the speed of Bus A.
- Both buses meet each other at S3.
- The distance between S1 and S3 is 60% of the distance between S1 and S2.


To find the time taken by Bus A for its journey from S1 to S2, we need to consider the relative speed of the two buses. Let's assume the speed of Bus A is x km/h, then the speed of Bus B would be 0.75x km/h (75% of x).


We can use the formula time = distance/speed to calculate the time taken by each bus for their respective journeys.

- Distance between S1 and S3: Let's assume it as d km.
- Distance between S1 and S2: Let's assume it as D km.


- From S1 to S3: The distance is 0.6D km. Time taken = (0.6D)/x hours.
- From S3 to S2: The distance is 0.4D km. Time taken = (0.4D)/x hours.


- From S2 to S3: The distance is 0.4D km. Time taken = (0.4D)/(0.75x) hours.
- From S3 to S1: The distance is 0.6D km. Time taken = (0.6D)/(0.75x) hours.


The total time taken by both buses combined is the sum of their individual times.

Total time = (0.6D)/x + (0.4D)/x + (0.4D)/(0.75x) + (0.6D)/(0.75x)

Simplifying the above expression:

Total time = (1.8D + 0.6D + 0.8D + 1.2D)/(1.5x)
= 4.4D/(1.5x)


Since both buses meet each other at S3, the time taken by both buses must be equal. Therefore, we can equate the total time taken by both buses:

(0.6D)/x + (0.4D)/x + (0.4D)/(0.75x) + (0.6D)/(0.75x) = 2(0.6D)/

Given information:
- Bus A left station S1 at 11 am for station S2.
- Bus B, having a speed 75% of the speed of A, left station S2 for station S1 at 12 pm.
- The two buses meet each other at station S3.
- The distance between S1 and S3 is 60% of the distance between S1 and S2.

To Find:
The time taken by bus A for its journey from S1 to S2.

Assumptions:
- Let the distance between S1 and S2 be D km.
- Let the speed of bus A be V km/h.
- Let the speed of bus B be 0.75V km/h.

Calculations:

1. Time taken by bus A from S1 to S3:
- Let the distance between S1 and S3 be 0.6D km.
- The time taken by bus A to cover this distance is given by the formula: Time = Distance / Speed.
- Substituting the values, we have: Time(A-S1-S3) = (0.6D) / V.

2. Time taken by bus B from S2 to S3:
- The distance between S2 and S3 is the same as the distance between S1 and S3, i.e., 0.6D km.
- The time taken by bus B to cover this distance is given by the formula: Time = Distance / Speed.
- Substituting the values, we have: Time(B-S2-S3) = (0.6D) / (0.75V).

3. Total time taken by bus A from S1 to S2:
- The time taken by bus A from S1 to S3 is already calculated as (0.6D) / V.
- The time taken by bus B from S2 to S3 is also calculated as (0.6D) / (0.75V).
- The total time taken by bus A from S1 to S2 is the sum of these two times.
- Substituting the values, we have: Total Time(A-S1-S2) = (0.6D) / V + (0.6D) / (0.75V).

4. Given Information:
- Bus B left station S2 for station S1 at 12 pm, which means it traveled for 1 hour less than bus A.
- This implies that the total time taken by bus A from S1 to S2 is 1 hour more than the time taken by bus B from S2 to S3.

5. Equation:
- From step 3, we have the equation: Total Time(A-S1-S2) = (0.6D) / V + (0.6D) / (0.75V).
- From step 4, we have the equation: Total Time(A-S1-S2) = Time(B-S2-S3) + 1.

6. Solving the Equation:
- Equating the two equations, we have: (0.6D) / V + (0.6D) / (0.75V) = (0.6D) /