You really don't need Rails for this task although its true you could
make it in Rails if you want. As some other people said, you can do this
could just find someone technically savvy to do it for you. Based on
your description making this would only take me about a couple of hours
and I am sure it would be the same for any other novice-intermediate
learning HTML since it is so easy even for a total novice. Once you have
laid out the page in HTML (setting up how you want it to look visually),
start/finished button) shouldn't be too hard.
It almost seems like this would be overkill for using Rails unless you
need to store results or collect some sort of data / graph / visualize
data in which it might make more sense.
Either way, good luck.