3. A train passes a pole in 5 s. How long (in seconds) will it take for the train and an electric train to pass each other, if the speed of the train is twice the speed of the electric train, and the length of the train is three times the length of the electric train
3. Let $v_{1}, l_{1}$ be the speed (in m/s) and length (in m) of the train; $v_{2}, l_{2}$ be the speed (in m/s) and length (in m) of the electric train. According to the problem, $v_{2}=\frac{1}{2} v_{1} ; l_{2}=\frac{1}{3} l_{1}$. Knowing that the train passes a pole in 5 seconds, we have $\frac{l_{1}}{v_{1}}=5$. To determine the time it takes for the train and the electric train to pass each other, we need to divide their total length by their combined speed (from the problem, it is clear that the train and the electric train are moving towards each other), that is, this time is $\frac{l_{1}+l_{2}}{v_{1}+v_{2}}=\frac{l_{1}+\frac{1}{3} l_{1}}{v_{1}+\frac{1}{2} v_{1}}=\frac{8 l_{1}}{9 v_{1}}=\frac{8 \cdot 5}{9}=\frac{40}{9}$ (s)

Answer: $\frac{40}{9}$