It is a translation mistake.

Your idea Is correct, they will be both walking for a while until Y reaches the bike and catches up with X. **X then rides the bike again to the distance (d).** Such Is the cycle.

Let's just focus on the bike ...

From start ... Relative speed between X and Y is 10 Km/Hr , distance between them is d when bike is laid down , so time is d/10 Hrs

Then the bike has zero speed for d/5 Hrs .. ( the walker travels d at 5 km/hr to reach the bike)

Then the bike travels the distance between X and Y in d/10 Hrs and X and Y are together again ....

This is the cycle , the bike travels at 15Km /Hr for two periods of d/10 = d/5Hrs ..... and is still for d/5Hrs

So the average speed of the bike is 7.5Km/Hr ... and is not dependent on d , so this should answer part (a) of the question ....

b) Determine conditions under which both X and Y will get to B at the same time and calculate number of cycles needed to accomplish this....

For X and Y to reach B at the same time a complete number of cycles must have occurred ...

How much distance is one cycle ??? there should be enough information in this post to find this distance ...

If the cycle distance divides into 5 (distance from A to B) and gives a whole number then X and Y will meet at B