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First I thought the question was when would they pass the same location at the same time, and there is not enough information for that. But there is a 100% probability of such an incident occurring. A distance-time graph shows that when this occurs is dependent upon the velocity history of the car in both journeys, but it also shows that it will always occur.
Richard L. Bowman
Bridgewater College, VA, USA
Brian Whatcott [firstname.lastname@example.org] wrote on Saturday, June 21, 2008:
Click and Clack offered a version of the following puzzler
A family of four drove up the west coast 400 miles on Saturday,
starting at 8 a.m. They arrived at their destination at 4 p.m.
Three of them returned home the following day by the same route,
in the same car, starting at 11 a.m. Sunday.
The question: what is the probability that the car passed the
same spot at the same time of day, going both ways?
I was surprised that the answer was not immediately obvious.
To me at least.
The idea of space time diagrams came to mind.
Brian Whatcott Altus OK Eureka!