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The Sunrize Izumo, one of the last two remaining japanese sleeper trainshas something like that - from necessity. The on board water supply is limitted, so a vending mashine on board sells a given ammount of shower-cards, that let you shower for an alotted number of minutes, counted with second precission on a LED display in the shower.

This way the on board shower will not run out of water & you get the opportunity to do a shower speedrun. :)

probably depends on how meaningful the cost of utilities is to you. I try to use AC and heat sparingly just because I hate the idea of waste; it really annoys me if I have to turn on the heat a few nights later because I turned on my AC too early. but my whole utility bill is ~$70/month. I don't really care too much about saving 10-20% of that.

You’re probably right! Why not show both?

water is far too cheap for this to work

Depends on your location. For example, this could be very effective someplace like the southwest US.

Obviously it wouldn't work everywhere, but it could work for a few people I know personally.