Question 119
A village $M$ is on the road between the villages $A$ and $B$. The distance between $A$ and $M$ is twice as long as the distance between $B$ and $M$. Ann, Bob and Tom live in $A$, $B$ and $M$ respectively. One day Tom invites Ann and Bob to a game of chess. Ann and Bob walk along the road with constant and equal speeds, and they start from their villages at the same time. Tom has a motorbike. Tom has two possibilities: he rides towards Ann and brings her to $M$ and after that he rides towards Bob and brings him to $M$, or he rides towards Bob and brings him to $M$ and after that he rides towards Ann and brings her to $M$. The total time in the first case differs from the total time in the second case by 2.4 minutes. The speed of the motorbike is nine times the speed of the pedestrians.
How long does it take Ann to reach $M$ on foot?
How long does it take Ann to reach $M$ on foot?