OPM 2013 Problem 2

In the morning, three people, $A$ , $B$ and $C$ run in a same line at a beach in Albufeira. Some day, the three people were in the same point of the beach and then they started to run at the same time, but in different velocities. For each person, the velocity was constant. When someone arrived in an extreme of the beach, he/she turned back and runned in the opposite direction. In the moment in that the three people were in the same point of the beach again, the running finished. Not counting with the beginning and the final of the running, $A$ met $B$ six times and $A$ met $C$ eight times. How many times did $B$ and $C$ meet?