A boy is standing at a bus stop and is freezing, but the bus is not there. He wants to walk to the next stop. The boy runs four times slower than the bus and can see the bus from a distance of 2 km. The next stop is exactly 1 km away. Does it make sense to go, or is there a risk of missing the bus?
Let the boy walk to the next stop and at some point notice the bus. The speed of the bus is four times the speed of the boy, so in the same amount of time, the bus covers a distance four times greater. If they are moving towards each other, before meeting the bus, the boy will run one-fifth of 2 km, that is, $2 / 5$ km. This means that if he is no more than $2 / 5$ km away from the stop, the boy can catch the bus by running back. If the bus is catching up to the boy, the boy will manage to run one-third of 2 km (while the bus covers $4 / 3$), that is, $2 / 3$ km before the bus catches up to him. This means that he can catch the bus if there is no more than $2 / 3$ km left to the next stop. Since $2 / 3 + 2 / 5 > 1$, the boy will always have a chance to catch the bus, and it makes sense to go.

## Answer

It makes sense to go.