A man walking at speed v and an old man walking at speed 0.5v enter a circular park through the same gate and walk in opposite directions. If the man completes two rounds and exits through the same gate, how many times will they meet each other?
Solution
Let the circumference of the circular park be C.
Distance covered by the man = 2C
Distance covered by the old man = C
Relative distance covered = 3C
One meeting takes place after one relative round or when C relative distance is covered.
So, three meetings would take place after 3C relative distance is covered.
This means that just when the man is about to exit from the gate after two rounds, the old man also reaches the gate after one round.
The three meetings will be angularly equispaced. In other words there will be a meeting after every 120 degree angle.
