# Practical Relativity

Here is a small problem from the classical B. A. Kordemsky's collection:

Two school girls were traveling from the city to a dacha (summer cottage) on a suburban train.

"I notice," one of the girls said, "that the dacha trains coming in the opposite direction pass us every 5 minutes. What do you think - how many dacha trains arrive in the city in an hour, given equal speeds in both directions?"

"Twelve, of course," the other girl answered, "because 60 divided by 5 equals 12."

The first girl did not agree. What do you think?

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Copyright © 1996-2017 Alexander Bogomolny

Two school girls were traveling from the city to a dacha (summer cottage) on a suburban train.

"I notice," one of the girls said, "that the dacha trains coming in the opposite direction pass us every 5 minutes. What do you think - how many dacha trains arrive in the city in an hour, given equal speeds in both directions?"

"Twelve, of course," the other girl answered, "because 60 divided by 5 equals 12."

The first girl did not agree. What do you think?

### Solution

If the girls were on a standing train, the second girl's calculations would have been correct,correct,wrong, but their train was moving. After passing one train, it took 5 minutes to meet the next one, but then it took the latter 5 minutes to reach the spot where the girls met the first train. So the time between trains in the same direction is 10 minutes, not 5, and only 6 trains per hour arrive in the city.

Here's a rephrase. The relative speed of two trains moving towards each other is double,double,the same,triple the speed of either one of them. Whatever the distance, it is covered by a "coupled" train twice as fast,slow,fast as by a single train. For example, the distance between two consecutive meetings of the trains is covered by a train in one direction in 10 minutes, not 5!.

### References

- B. A. Kordemsky,
*The Moscow Puzzles*, Dover, 1972, #63

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