[ Motion problems ]

Sasha and Ilya had to run 600 meters. But Sasha ran the first half of the time and walked the second half. And Ilya ran the first half of the distance and walked the second half. They started and finished at the same time. Both of them walk at a speed of 5 km/h. At what speed did Ilya run, if Sasha ran at a speed of 10 km/h?
Since Sasha runs twice as fast as he walks, he ran twice the distance he walked, which is 400 m. Since the boys walk at the same speed, they walked the last 200 m together. Therefore, while Sasha ran 400 m, Ilya ran 300 m and walked 100 m. While Ilya walked 100 m, Sasha ran 200 m. And while Sasha ran $400-200=200$ m, Ilya ran 300 m. This means Ilya runs one and a half times faster than Sasha, that is, at a speed of 15 km $/$ h

## Answer

15 km $/$ h.