If you are purchasing a home from an actual seller, it can be very quick. If you are buying a foreclosure from a bank or investor, it can take up to 2 weeks; and if you are purchasing a short sale, it can take up to 3-4 months to get full approval from the bank. In that case, it doesn't matter when the homeowner accepts it, the offer must be ratified by the bank/investor.
Hope this helps!
Lancaster, Ca 93534