# Rat maze?

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A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.

What is the expected amount of time it will take for the rat to finish the maze?

arjun00848 Expert Asked on 20th August 2015 in

x = 0.25 * 5 + 0.25 (x + 8) + 0.25 * 3 + 0.25 (x + 2)
x = 1.25 + 0.25x + 2 + 0.75 + 0.25x + 0.5
x = 4.5 + 0.5x
0.5x = 4.5
x = 9

Ralph Aldanese Scholar Answered on 4th March 2016.

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