Question on Speed and Distance

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X, Y and Z move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. X and Y move in the same direction but Z moves in opposite direction. If they all start at the same time and from same place, how many times will X and Z meet anywhere on the path by the time X and Y meet for the first time anywhere on the path ? I was getting the answer as 7 times but the correct answer is 8. Am I wrong ? Can someone explain ?

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I think it is a fencepost error. X and Z meet once at the start, after zero hours, and the seven more you calculated.