This is a matter of partial pressure.
That is, the state of a substance isn't binary, liquid below the boiling point and gaseous above. Rather, an equilibrium between a liquid and its vapour can exist at varied temperatures. The equilibrium vapour pressure increases (quickly) with the temperature.
The boiling point is only the temperature for which the equilibrium vapour pressure equals the ambient pressure. Above this temperature, the vapour has enough pressure to push the liquid to the sides to make bubbles. Hence the name "boiling point", not some undefinable "vapour point". And the boiling points depends on the ambient pressure.
So evaporation occurs below the boiling point too, it only produces less vapour pressure than the ambient pressure, and this vapour is diluted in the ambient gas that makes most of the ambient pressure. This happens when oceans too cold to boil inject humidity in the atmosphere. Or when you see vapour (or rather condensing vapour) over a pan before the water boils.
Now if you boil two mixed liquids, the liquid with a higher boiling point contributes to the evaporation too, more so if the temperature is near to its boiling point. So for the vapour to be purer, you need a big difference between the boiling points. 40K is just one arbitrary value to get "enough" difference in the vapour pressures.
This implicitly supposed little interaction between the substances. Counter-example: a solution of ammonia in water doesn't produce the ammonia vapour pressure corresponding to the equilibrium vapour pressure of liquid ammonia.