1. Petya came to the bus stop of the bus going to school with stops equally spaced from each other, and, not seeing the bus on the road, decided to run and get on the bus at the next stops along the way to school. Petya ran in such a way that at any moment he could notice the appearance of the bus on the road behind him. Seeing the bus, Petya can turn back or maintain his direction of movement. It is known that the speed of the bus is 4 times greater than Petya's running speed, and he can see the bus at a distance of no more than 1.5 km. Find the greatest value of the distance between stops, such that regardless of whether Petya turns back upon discovering the bus or not, he will be able to get on the bus at a stop.
Answer: $a_{\max }=0.8$ km