The boy travels from A to B at 6 km/h and returns at 9 km/h. The total time taken is 1 hour 15 minutes.
Convert 1 hour 15 minutes to hours:
1+6015=1.25 hours
Let the distance between A and B be d km.
Time taken to go from A to B:
6d hours
Time taken to return from B to A:
9d hours
Total time:
6d+9d=1.25
The LCM of 6 and 9 is 18.
6d=183d
9d=182d
183d+182d=1.25
185d=1.25
185d=1.25
5d=1.25×18
5d=22.5
d=522.5
d=4.5
Therefore, the distance between A and B is 4.5 km.