Water evaporation problem. Exercise from Feynman's lectures

I read lectures of Richard Feynman and try to solve problems for more deep understanding themes.
And I have some problem with calculating water evaporation.

It is text of exercise:
A glass full of water is left standing on an average outdoor window in California.
a) How long do you think it would take to evaporate completely?
b) How many molecules $$cm^{-2} s^{-1}$$ would be leaving the water glass at this rate?
c) Briefly discuss the connection, if any, between your answer to part (a) above and the average rainfall over the earth

I think calculation the velocity of evaporation at first is the most easy way for solving this problem. So I break glass into layers, every layer equals a high of one water molecule ($$2.8\times10^{-8}cm$$). I know the number of molecules in 1 $$cm^3$$ in the water ($$3\times10^{22}$$). The average diameter of glass is (6.75 $$cm$$) and I suppose that it is surface. Next I look at surface layer in 2 dimensional view. So each molecule moves in 4 main directions. I suppose that in $$\frac{1}{4}$$ ways molecule goes into the air. I take normal humidity of air like 60%. But I don't know velocity of this molecule that I need for calculating rate of evaporation. This velocity is equal the temperature (because temperature is only movement of molecules).

Should I use the temperature in joule? Will commensurability be right in this way?

Can someone help me with algorithm of solution? I want understand analytical part of this problem. I don't sure that my method is right.