Set Theoryhard
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Two pipes P1P_1 and P2P_2 fill a tank. P1P_1 fills it in t1{2,4}t_1 \in \{2, 4\} hours and P2P_2 fills it in t2{3,6}t_2 \in \{3, 6\} hours. If t1,t2t_1, t_2 are chosen randomly, what is the set of possible times t=t1t2t1+t2t = \frac{t_1 t_2}{t_1 + t_2} to fill the tank?