Ping and Pong are standing back to back at a train station. Then a train passes with a constant unknown velocity. When the beginning of the train is exactly "next to" Ping and Pong they start walking with the same constant unknown velocity in opposite directions. Ping walks exactly parallel to the train, while Pong walks 180° to that direction. When the end of the train passes Pong he stops walking. A bit later Ping does the same when the end of the train passes him. They measure then how much they walked. Pong walked 30 meters and Ping walked 40 meters. How long is the train?

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Originally posted by Fat Lady 1) Note that Ping manages to walk 10 metres after the end of the train passes Pong before the end of the train reaches him.

2) The distance between Ping and Pong is then 70 metres.

3) Thus the train has travelled 70m in the time it took Ping to travel 10m and so is going 7 times faster.

4) Call the speed of Ping and Pong 'v', making the speed of th ...[text shortened]... p in 10) and 14) equal to each other gives L / 24v = 10 / v which simplifies to L = 240.

Originally posted by Fat Lady 1) Note that Ping manages to walk 10 metres after the end of the train passes Pong before the end of the train reaches him.

2) The distance between Ping and Pong is then 70 metres.

3) Thus the train has travelled 70m in the time it took Ping to travel 10m and so is going 7 times faster.

4) Call the speed of Ping and Pong 'v', making the speed of th ...[text shortened]... p in 10) and 14) equal to each other gives L / 24v = 10 / v which simplifies to L = 240.