A train traveling at a constant speed takes a passenger from Grover to Auburn, stopping first at Tyler and next at Elena before arriving at Auburn. While it takes the same time to travel from Tyler to Elena as it does to travel from Grover to Tyler, it takes only one-fourth the time of either of those trips to travel from Elena to Auburn. How far is the ride from Tyler to Auburn if the entire trip is 450 miles? Name a geometric postulate or theorem used to find the solution.

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