Well if its from 3cm then my labour with my son was probably less than an hour. I say probably as I wasn't subject to any internal exams due to the lovely approach of the midwifes who said it wasn't necessary.
I had been in early labour from 3pm and by around 9pm we called hospital (MLU) - I was only having a contraction every 10 mins, but they were getting stronger, and I had lost my mucus plug. It was a sunday night and they said all three rooms were empty so we may as well come in even if it was a bit early.
When I arrived (only one mild contraction whole way there, 15 mins in car) and I hadn't even bothered putting on tens machine - they took one look at me, said not in established labour, no need for internal, just took my temperature, blood pressure and checked babies position and heartbeat (handheld doppler). They then left us on our own (which we were happy with) - said it was too early to get into pool. I have no idea how dilated I was but wouldn't have been surprised if not very at all - I am sure they would have sent us home had they been busy.
However, within 20 mins of arrival my waters went and suddenly was have strong contractions every 3 mins lasting minute and a half! DS born within 90 mins of waters going. With my DD (first labour) went from 1cm to 10cm in around 3 hours, which is quite quick for a first labour.
This time I am going to refuse a VE on arrival because its not relevant AT ALL ie if I am only 1cm dilated, I could still have the baby within the hour, and its 20 mins home and 20 mins back if they try and sent me home.