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Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other?
Distance between A-B , A-C, C-B is 180, 120 and 60 km respectively.
Let x be the distance from A where the 2 trains meet.
According to given condition we have
$$\frac{x}{70}=\frac{60}{50} + \frac{1}{4} + \frac{120-x}{50}$$.
Solving the equation we get x around 112 km.
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