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Water evaporation problem. Homework 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.

There is a sum:
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?

I think more easy way for solving this sum is calculate the velocity of evaporation first. So I take a glass and break it into layers, every layer have a high of one water molecule ($2.8\times10^{-8}cm$). I know how many molecules are in 1 $cm^3$ in water ($3\times10^{22}$). I found average diameter my glass (6.75 $cm$) and suppose that it is surface. Next I look at surface layer in 2 dimensional view. So molecules move 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), but there is some trouble with commensurability. And I don't know how can I find it.

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