A variant of the Test:Harness should be able to do this. If submitteers just provide the snippet of code, then the harness can do all the timing, generate statistics and ensure common test files, etc.
There are also some subtleties between improvements in speed derived from better algorithms and those derived from implementing the same algorithm better.

For example one race could be "Write a fast quicksort routine", vs. "write a fast sort routine". In the first case, the winner will be the one who programs the algorithm best, in the latter case it will be the one who comes up with the algorithm best suited to the data.

In some cases, whether the test data is given with the challenge will be important to the outcome.

Re: machine variations: I wouldn't expect the machine variation to matter as much as the algorithm / coding variation. I.e. the fastest algorithm one one machine is likely to be the fastest on any machine.
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Brovnik.