Chris - Well the answer is about 5 mm per minute, and it's in fact, five body lengths of the sperm per second.

So if you scaled them up to the size of a salmon, that would be the equivalent of the salmon swimming along at 500 miles an hour, or a whale doing 15,000 miles an hour.*

So the sperm are pretty snappy. They get to the egg pretty fast, certainly within a day or so.

How do they find the egg? They recognise it by two means: one is a thermal gradient. They follow temperature so they know that the body gets warmer the further in they go. So they follow the thermal gradient. The second is that the egg oozes out various attractive molecules, in the same way that various inflammatory things attract the immune system in. This pulls the sperm towards the egg because they follow their noses, quite literally...

[*Thank you to the visitor who pointed out that this is a slight exaggeration!]