Vapour Pressure and Equilibrium I found this questions on a YouTube lesson and I'm confused with the answers they have given:  

"A liquid in its equilibrium with its vapour is in a sealed container at a fixed temperature. The volume of the container in suddenly increased."  

Questions:
a) What are the changes in the rate of evaporation and condenation? 

b) How will the equilibrium be restored ultimately and what will be the final vapour pressure?

Answers:
a) Rate of evaporation depends on the substance and applied temperature so it will be unchanged and rate of condensation will decrease as vapour pressure is decreased. (Why? Is it true?)  

b) They say that the vapour pressure will be restored and the rate of condensation and evaporation will be equal as the system reaches the equilibrium. (But they said that rate of condensation will decrease and rate of evaporation will stay the same. Then how will they be equal?)

Please clarify the whole thing.
The key missing piece is identifying when the system is in equilibrium. When you suddenly increase the volume, the system is temporarily not in equilibrium. In this situation, a few things will happen:


The rate of evaporation won't change for the reason given
The vapor pressure will decrease. As a first approximation, we can use the ideal gas law to see how. $PV=nRT$ can be rearranged as $P=nRT/V$. The number of moles ($n$), gas constant ($R$), and temperature ($T$) will stay the same (this last one in particular isn't really true, but it doesn't change the qualitative result). Then, if the volume increases, the pressure will decrease.
Since the pressure has decreased, the rate at which gaseous molecules bump into the liquid decreases. The ones that do bump into the liquid will condense into the liquid at the same rate. The total condensation rate is the product of those two factors, so the condensation rate will decrease.


Now, since the evaporation rate is the same as it was before, but the condensation rate will go down, we will get a net evaporation. As more liquid becomes gas, the vapor pressure will increase. As the vapor pressure increases, the condensation rate will increase, for the reasons discussed above. Once the vapor pressure is high enough that the condensation rate equals the evaporation rate, then we will have a dynamic equilibrium.