lean_workbook_plus_64781

Another way: Suppose $E$ is the expected time. Then $E$ is equal to $\dfrac{1}{3} \cdot 2$ (time if he picks the first opening), plus $\dfrac{1}{3} \cdot (3 + E)$ (time if he picks the second opening; the plus E is because he's at the exact same situation after he traveled 3 hours), plus $\dfrac{1}{3} \cdot (5 + E)$ (time if he picks the third opening, see above). So $E = \dfrac{2 + (3 + E) + (5 + E)}{3}$ $3E = 10 + 2E$ $E = 10$ So he will need 10 hours on average.