1. Kolya went to the store in the neighboring village on an electric scooter at a speed of 10 km/h. Having traveled exactly one third of the entire distance, he realized that with the previous speed, he would arrive exactly when the store closes, and he doubled his speed. But when he had traveled exactly $2 / 3$ of the entire distance, the scooter broke down, and Kolya walked the remaining part of the way. At what speed did he walk if he arrived exactly when the store closed?
Answer: $6 \frac{2}{3}$ km/h.

Solution. Let the distance to the village be $3 x$ km. If Kolya had traveled the entire time at a speed of $10 \mathrm{km} /$ h, he would have spent $3 x / 10$ hours on the road. This is the time from his departure to the store's closing. The first third of the distance Kolya traveled in $x / 10$ hours. Doubling his speed, Kolya traveled the second third of the distance in $x / 20$ hours. Thus, for two-thirds of the distance, he spent $x / 10 + x / 20 = 3 x / 20$ hours. Therefore, $3 x / 10 - 3 x / 20 = 3 x / 20$ hours remained until the store's closing, and during this time he managed to travel $x$ km. Thus, he traveled at a speed of $x: \frac{3 x}{20} = \frac{20}{3}$ km/h.