A train takes 22 seconds to cross a bridge completely while an athlete takes 60 seconds to cross the same bridge. If the train can overtake the athlete in 12.5 seconds, then, in how many seconds can the train cross the athlete if they move in opposite directions?

Let the length of the bridge be L, and the length and speed of the train be l and v. The time taken by the athlete to cross is 60 seconds, so L = 60u. The total distance for the train is L + l = 22v. The relative speed when overtaking is v - u, and we have l = 12.5(v - u). Substituting L = 60u into the bridge crossing gives l = 22v - 60u. Setting the two equations for l equal gives 12.5v - 12.5u = 22v - 60u, which simplifies to 47.5u = 9.5v, so u = v/5. This means the athlete's speed is 20 percent of the train's speed. When moving in opposite directions, their relative speed is v + u = 1.2v. The time to cross each other is the train's length divided by this relative speed: l / (1.2v). From the overtaking equation, l / (0.8v) = 12.5. Therefore, l / v = 10, and dividing by 1.2 gives a crossing time of 8 and one-third seconds.

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