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Back Seat Mathematician

A math teacher ... was driving along a country road ...when she noticed that the passing trees had been planted an equal distance apart. So she glanced down at her clock when the car was midway between trees and counted the number that she passed in one minute.

"How interesting!" she said to herself afterward. "When I multiply the number of trees by 10, the result equals the speed of my car in miles per hour."

Assuming that the speed of the car was constant and that the minute ended midway between trees, how far apart were they?


Source: Marilyn vos Savant' Column, Parade, December 25, 2005.

Hint: Focus on the units involved...e.g. miles/hour, miles/tree, etc.


Solution Commentary: Marilyn'solution...convoluted as usual: "If X is the number of trees passed in one minute, 60X is the number passed in one hour. As we know the car is traveling 10X miles per hour, we also know that in 10X miles it will pass 60X trees. So, in one mile, the car will pass (60X)/(10X) (trees per hour) / (miles per hour)trees. That number is 6: The trees are 1/6th of a mile apart.

Can you find a more straight forward solution...I expect so...and it probably lies behind Door #3.