1. Boy Tolya loves to swim. When he comes to one grandmother's cottage, he swims in the Volkhov and floats downstream from one beach to another in 18 minutes. On the way back, it takes him exactly 1 hour. When he came to another grandmother's cottage, he swam the same distance downstream in the Luga River in 20 minutes. How much time will it take him to return back?
Answer: 45 minutes.

Solution. Let the distance between the beaches be $x$ km. Then in Volkhov, Tolya swims downstream at a speed of $x / 18$ km/min, and upstream at a speed of $x / 60$ km/min. Therefore, Tolya's own speed is $\frac{1}{2}(x / 60 + x / 18) = 13 x / 360$ km/min. In Luga, Tolya swims downstream at a speed of $x / 20$ km/min. Thus, the speed of the current in Luga is $x / 20 - 13 x / 360 = 5 x / 360$ km/min. Therefore, Tolya's speed against the current in Luga is $13 x / 360 - 5 x / 360 = x / 45$ km/min. Hence, Tolya will swim $x$ km against the current in Luga in 45 minutes.