Problem 2. Baba Yaga must arrive at Bald Mountain exactly at midnight. She calculated that if she flies on a broom at a speed of 50 km/h, she will be 2 hours late, and if she flies on an electric broom at a speed of 150 km/h, she will arrive 2 hours early. To arrive at Bald Mountain exactly on time, Baba Yaga used a wand. At what time did Baba Yaga take off and at what speed did she fly on the wand?
Answer: At 20:00 at a speed of 75 km/h.

Solution. The electric broom flies three times faster than the cauldron, and at the same time, it saves 4 hours of time. This means that two-thirds of the flight time in the cauldron is 4 hours, the entire flight in the cauldron would have taken 6 hours, and the entire flight on the electric broom would be three times less, that is, 2 hours. In this case, Baba Yaga would have taken off 6 hours before two o'clock at night, that is, at 20:00 in the evening. To arrive on time, Baba Yaga needs to spend 4 hours in flight, which is twice as long as on the electric broom. This means that flying on the broom needs to be twice as slow as on the electric broom, that is, at a speed of 75 km/h.